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References

Published online by Cambridge University Press:  15 December 2020

Ariel Amir
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Harvard University, Massachusetts
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Thinking Probabilistically
Stochastic Processes, Disordered Systems, and Their Applications
, pp. 225 - 231
Publisher: Cambridge University Press
Print publication year: 2020

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References

Addario-Berry, L. and Reed, B. A., Ballot theorems, old and new, in: Horizons of Combinatorics (pp. 9–35), Springer, Berlin, Heidelberg (2008).Google Scholar
Ambegaokar, V., Halperin, B. I., and Langer, J. S., Hopping conductivity in disordered systems, Physical Review B, 4, 8, 2612 (1971).Google Scholar
Ambegaokar, V., Halperin, B. I. Nelson, D. R., and Siggia, E. D., Dynamics of superfluid films, Physical Review B, 21, 5, 1806 (1980).Google Scholar
Amir, A., Cell size regulation in bacteria, Physical Review Letters 112, 20, 208102 (2014).Google Scholar
Amir, A., An elementary renormalization-group approach to the Generalized Central Limit Theorem and Extreme Value Distributions, Journal of Statistical Mechanics: Theory and Experiment, 1, 013214 (2020).Google Scholar
Amir, A. and Balaban, N. Q., Learning from noise: how observing stochasticity may aid microbiology, Trends in Microbiology, 26, 4, 376 (2018).Google Scholar
Amir, A., Hatano, N., and Nelson, D. R., Non-Hermitian localization in biological networks, Physical Review E, 93, 4, 042310 (2016a).Google Scholar
Amir, A., Krich, J. J., Vitelli, V., Oreg, Y., and Imry, Y., Emergent percolation length and localization in random elastic networks, Physical Review X, 3, 2, 021017 (2013a).Google Scholar
Amir, A., Lahini, Y., and Perets, H. B. Classical diffusion of a quantum particle in a noisy environment, Physical Review E, 79(5), p.050105 (2009).Google Scholar
Amir, A., Lemeshko, M. and Tokieda, T., Surprises in numerical expressions of physical constants, The American Mathematical Monthly, 123, 6, 609 (2016b).Google Scholar
Amir, A., Oreg, Y., and Imry, Y., 1/f noise and slow relaxations in glasses, Annalen der Physik, 18, 12, 836 (2009).Google Scholar
Amir, A., Oreg, Y., and Imry, Y., Localization, anomalous diffusion, and slow relaxations: A random distance matrix approach, Physical Review Letters, 105, 7, 070601 (2010).Google Scholar
Amir, A., Oreg, Y., and Imry, Y., On relaxations and aging of various glasses, Proceedings of the National Academy of Sciences, 109, 6, 1850 (2012).Google Scholar
Amir, A., Paulose, J., and Nelson, D. R., Theory of interacting dislocations on cylinders, Physical Review E, 87, 4, 042314 (2013a).Google Scholar
Anderson, G. W., Guionnet, A., and Zeitouni, O., An Introduction to Random Matrices, Cambridge University Press (2010).Google Scholar
Anderson, P. W., Absence of diffusion in certain random lattices, Physical Review, 109, 5, 1492 (1958).Google Scholar
Anderson, P. W., More is different, Science, 177, 4047, 393 (1972).Google Scholar
Arfken, G. B., Weber, H. J., and Harris, F. E., Mathematical Methods for Physicists, A Comprehensive Guide, 7th edn, New York: Academic (2012).Google Scholar
Axler, S. J., Linear Algebra Done Right, New York: Springer (2015).Google Scholar
Bachelier, L., Theory of speculation (1900) in: P. Cootner, ed., The Random Character of Stock Market Prices, MIT Press (1964).Google Scholar
Baik, J., Borodin, A., Deift, P., and Suidan, T., A model for the bus system in Cuernavaca (Mexico), Journal of Physics A: Mathematical and General, 39, 28, 8965 (2006).Google Scholar
Bardou, F., Bouchaud, J.P., Aspect, A. and Cohen-Tannoudji, C. Lévy Statistics and Laser Cooling: How Rare Events Bring Atoms to Rest, Cambridge University Press (2002).Google Scholar
Battersby, S., Statistics hint at fraud in Iranian election, New Scientist 202, 2714, 10 (2009).Google Scholar
Bazant, M. Z., Largest cluster in subcritical percolation, Physical Review E, 62, 2, 1660 (2000).Google Scholar
Bertin, E. and Györgyi, G., Renormalization flow in extreme value statistics, Journal of Statistical Mechanics: Theory and Experiment, 2010, 08, 08022 (2010).Google Scholar
Bertrand, J. Calcul des probabilités. Gauthier-Villars (1907).Google Scholar
Billingsley, P., Probability and Measure. John Wiley and Sons (2008).Google Scholar
Black, F. and Scholes, M., The pricing of options and corporate liabilities, Journal of Political Economy 81, 637 (1973).Google Scholar
Blitzstein, J. K. and Hwang, J., Introduction to Probability, Chapman and Hall/CRC (2014).CrossRefGoogle Scholar
Bohigas, O., Giannoni, M. J., and Schmit, C., Characterization of chaotic quantum spectra and universality of level fluctuation laws, Physical Review Letters, 52, 1, 1 (1984).Google Scholar
Bressloff, P. C., Stochastic Processes in Cell Biology, Berlin: Springer (2014).Google Scholar
Brown, R. XXVII. A brief account of microscopical observations made in the months of June, July and August 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies, The Philosophical Magazine, or Annals of Chemistry, Mathematics, Astronomy, Natural History and General Science, 4, 21, 161 (1828).Google Scholar
Bruinsma, R., Halperin, B. I., and Zippelius, A., Motion of defects and stress relaxation in two-dimensional crystals, Physical Review B, 25, 2, 579 (1982).Google Scholar
Calvo, I., Cuchí, J. C., Esteve, J. G., and Falceto, F., Generalized central limit theorem and renormalization group, Journal of Statistical Physics, 141, 3, 409 (2010).Google Scholar
Calvo, I., Cuchí, J. C., Esteve, J. G., and Falceto, F., Extreme-value distributions and renormalization group, Physical Review E, 86, 4, 041109 (2012).Google Scholar
Chen, K., Ellenbroek, W. G., Zhang, Z., Chen, D. T., Yunker, P. J., Henkes, S., Brito, C., Dauchot, O., Van Saarloos, W., Liu, A. J. and Yodh, A. G., 2010. Low-frequency vibrations of soft colloidal glasses. Physical Review Letters, 105(2), p.025501.Google Scholar
Chechkin, A. V., Klafter, J., Gonchar, V. Y., Metzler, R., and Tanatarov, L. V., Bifurcation, bimodality, and finite variance in confined Lévy flights. Physical Review E, 67(1), p.010102 (2003).Google Scholar
Clauset, A., Kogan, M., and Redner, S., Safe leads and lead changes in competitive team sports, Physical Review E, 91(6), p.062815 (2015).Google Scholar
Coffey, W. T., Garanin, D. A., and McCarthy, D. J., Crossover formulas in the Kramers theory of thermally activated escape rates—application to spin systems, Advances in Chemical Physics, 117, 483 (2001).Google Scholar
Coffey, W. T., Kalmykov, Y. P., and Waldron, J. T., The Langevin Equation: with applications to stochastic problems in physics, Chemistry and Electrical Engineering. World Scientific (2004).Google Scholar
Datta, S. et al., Spatial fluctuations of fluid velocities in flow through a three-dimensional porous medium, Physical Review Letters, 111, 6, 064501 (2013).Google Scholar
Davidsen, J. and Schuster, H. G., Simple model for 1/f+ noise, Physical Review E, 65, 2, 026120 (2002).Google Scholar
Downey, A. B., The structural cause of file size distributions, in MASCOTS 2001, Proceedings Ninth International Symposium on Modeling, Analysis and Simulation of Computer and Telecommunication Systems, IEEE, pp. 361370 (2001)Google Scholar
Doyle, P. G. and Snell, J. L., Random Walks and Electric Networks, Mathematical Association of America (1984).Google Scholar
Dutta, P. and Horn, P. M., Low-frequency fluctuations in solids: 1/f noise, Reviews of Modern Physics, 53, 3, 497 (1981).Google Scholar
Dyson, F. J., A Brownian-motion model for the eigenvalues of a random matrix, Journal of Mathematical Physics, 3, 6, 1191(1962).Google Scholar
Ermann, L., Frahm, K. M., and Shepelyansky, D. L., Google matrix analysis of directed networks, Reviews of Modern Physics, 87, 4, 1261 (2015).Google Scholar
Feller, W., An Introduction to Probability Theory and Its Applications (Vol. 1), John Wiley and Sons (2008).Google Scholar
Feller, W., An Introduction to Probability Theory and Its Applications (Vol. 2), John Wiley and Sons (2008).Google Scholar
Filiasi, M., Livan, G., Marsili, M., Peressi, M., Vesselli, E. and Zarinelli, E., On the concentration of large deviations for fat tailed distributions, with application to financial data, Journal of Statistical Mechanics: Theory and Experiment, 9, P09030 (2014).Google Scholar
Fisher, R. A. and Tippett, L. H. C., Limiting forms of the frequency distribution of the largest or smallest member of a sample, in: Mathematical Proceedings of the Cambridge Philosophical Society (Vol. 24, No. 2, pp. 180–190). Cambridge University Press (1928).Google Scholar
Fortin, J. Y. and Clusel, M., Applications of extreme value statistics in physics, Journal of Physics A: Mathematical and Theoretical, 48, 18, 183001 (2015).Google Scholar
Gardiner, C., Stochastic Methods, Berlin: Springer (2009).Google Scholar
Ghosh, A., Chikkadi, V. K., Schall, P., Kurchan, J., and Bonn, D., 2010. Density of states of colloidal glasses. Physical Review Letters, 104(24), p.248305.Google Scholar
Gillespie, D. T., The mathematics of Brownian motion and Johnson noise, American Journal of Physics, 64, 3, 225 (1996).CrossRefGoogle Scholar
Ginibre, J., Statistical ensembles of complex, quaternion, and real matrices, Journal of Mathematical Physics 6, 3, 440 (1965).Google Scholar
Golding, I. and Cox, E. C., Physical nature of bacterial cytoplasm, Physical Review Letters, 96, 9, 098102 (2006).Google Scholar
Györgyi, G., Moloney, N. R., Ozogány, K., and Rácz, Z., Finite-size scaling in extreme statistics, Physical Review Letters, 100, 21, 210601 (2008).Google Scholar
Györgyi, G., Moloney, N. R., Ozogány, K., Rácz, Z., and Droz, M., Renormalization-group theory for finite-size scaling in extreme statistics, Physical Review E, 81, 4, 041135 (2010).Google Scholar
Hardy, G. H., Mendelian proportions in a mixed population, Science, 28, 706, 49 (1908).Google Scholar
Hassani, S., Mathematical Physics: A Modern Introduction to Its Foundations, Springer Science and Business Media (2013).Google Scholar
Hazut, N., Medalion, S., Kessler, D. A., and Barkai, E., Fractional Edgeworth expansion: corrections to the Gaussian-Lévy central-limit theorem, Physical Review E, 91, 5, 052124 (2015).Google Scholar
He, Y. et al., Random time-scale invariant diffusion and transport coefficients, Physical Review Letters, 101, 5, 058101 (2008).Google Scholar
Ho, P. Y. and Amir, A., Simultaneous regulation of cell size and chromosome replication in bacteria, Frontiers in Microbiology 6, 662 (2015).Google Scholar
Ho, P. Y., Lin, J., and Amir, A., Modeling cell size regulation: From single-cell-level statistics to molecular mechanisms and population-level effects, Annual Review of Biophysics, 47, 251 (2018).Google Scholar
Honerkamp, J., Stochastic Dynamical Systems: Concepts, Numerical Methods, Data Analysis. John Wiley and Sons (1993).Google Scholar
Hughes, B. D., Random Walks and Random Environments, Clarendon Press, Oxford (1996).Google Scholar
Imada, M., Fujimori, A., and Tokura, Y., Metal-insulator transitions, Reviews of Modern Physics, 70, 4, 1039 (1998).Google Scholar
Indyk, P., Stable distributions, pseudorandom generators, embeddings and data stream computation, in: Proceedings of the 41st Annual Symposium on Foundations of Computer Science, (pp. 189–197), IEEE (2000).Google Scholar
Jacobsen, J. L., Critical points of Potts and O(N) models from eigenvalue identities in periodic Temperley–Lieb algebras, Journal of Physics A: Mathematical and Theoretical, 48, 45, 454003 (2015).Google Scholar
Jehl, X., Sanquer, M., Calemczuk, R., and Mailly, D., Detection of doubled shot noise in short normal-metal/superconductor junctions, Nature, 405, 6782, 50 (2000).Google Scholar
Jona-Lasinio, G., Renormalization group and probability theory, Physics Reports, 352, 4–6, 439 (2001).Google Scholar
Katz, A. J. and Thompson, A. H., Quantitative prediction of permeability in porous rock. Physical Review B, 34, 11, 8179 (1986).Google Scholar
Keener, J. P., The Perron–Frobenius theorem and the ranking of football teams, SIAM Review, 35, 1, 80 (1993).Google Scholar
Klafter, J. and Sokolov, I. M., First Steps in Random Walks: From Tools to Applications, Oxford University Press (2011).Google Scholar
Knuth, D. E., The Art of Computer Programming (Vol. 1), Pearson Education (1997).Google Scholar
Knuth, D. E., The Art of Computer Programming, Vol. II, Seminumerical Algorithms, Addison Wesley, (1998).Google Scholar
Kohlrausch, R., Annals of Physics and Chemistry (Poggendorff) 91, 179 (1854).Google Scholar
Kostinski, S. and Amir, A., An elementary derivation of first and last return times of 1D random walks, American Journal of Physics, 84, 1, 57 (2016).Google Scholar
Koppes, L. J. et al., Correlation between size and age at different events in the cell division cycle of Escherichia coli, Journal of Bacteriology, 143, 3, 1241 (1980).Google Scholar
Krapivsky, P. L., Redner, S., and Ben-Naim, E., A Kinetic View of Statistical Physics. Cambridge University Press (2010).Google Scholar
Krbálek, M. and Seba, P., The statistical properties of the city transport in Cuernavaca (Mexico) and random matrix ensembles, Journal of Physics A: Mathematical and General, 33, 26, 229 (2000).Google Scholar
Kriecherbauer, T. and Krug, J., A pedestrian’s view on interacting particle systems, KPZ universality and random matrices, Journal of Physics A: Mathematical and Theoretical, 43, 40, 403001 (2010).Google Scholar
Lacroix-A-Chez-Toine, B., Grabsch, A., Majumdar, S. N., and Schehr, G., Extremes of 2d Coulomb gas: universal intermediate deviation regime, Journal of Statistical Mechanics: Theory and Experiment, 1, 013203 (2018).Google Scholar
Lam, H., Blanchet, J., Burch, D., and Bazant, M. Z., Corrections to the central limit theorem for heavy-tailed probability densities, Journal of Theoretical Probability, 24, 4, 895 (2011).Google Scholar
Langer, J. S., Statistical theory of the decay of metastable states, Annals of Physics, 54, 2, 258 (1969).Google Scholar
Le, J. L., Bazant, Z. P., and Bazant, M. Z., Lifetime of high-k gate dielectrics and analogy with strength of quasibrittle structures, Journal of Applied Physics, 106, 10, 104119 (2009).Google Scholar
Le, J. L., Bazant, Z. P., and Bazant, M. Z., Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: I. Strength, static crack growth, lifetime and scaling, Journal of the Mechanics and Physics of Solids, 59, 7, 1291 (2011).Google Scholar
Lehmann, N. and Sommers, H. J., Eigenvalue statistics of random real matrices, Physical Review Letters, 67, 8, 941 (1991).Google Scholar
Livan, G., Novaes, M., and Vivo, P., Introduction to Random Matrices, Springer (2018).Google Scholar
Majumdar, S. N. and Nechaev, S., Exact asymptotic results for the Bernoulli matching model of sequence alignment, Physical Review E, 72, 2, 020901 (2005).Google Scholar
Majumdar, S. N. and Schehr, G., Top eigenvalue of a random matrix: large deviations and third order phase transition, Journal of Statistical Mechanics: Theory and Experiment, 1, 01012 (2014).Google Scholar
Majumdar, S. N. and Vergassola, M., Large deviations of the maximum eigenvalue for Wishart and Gaussian random matrices, Physical Review Letters, 102, 6, 060601 (2009).Google Scholar
Manzato, C., Shekhawat, A., Nukala, P. K., Alava, M. J., Sethna, J. P., and Zapperi, S., Fracture strength of disordered media: Universality, interactions, and tail asymptotics, Physical Review Letters, 108, 6, 065504 (2012).Google Scholar
Marsden, J. E. and Hoffman, M. J., Elementary Classical Analysis, Macmillan (1993).Google Scholar
Matan, K., Williams, R. B., Witten, T.A. and Nagel, S. R., Crumpling a thin sheet, Physical Review Letters, 88, 7, 076101 (2002).CrossRefGoogle ScholarPubMed
Mathews, J. and Walker, R. L., Mathematical Methods of Physics, New York: WA Benjamin (1970).Google Scholar
May, R. M., Will a large complex system be stable?, Nature 238, 413 (1972).Google Scholar
Mehta, M. L., Random Matrices, Elsevier (2004).Google Scholar
Mertens, S. and Moore, C., Continuum percolation thresholds in two dimensions, Physical Review E, 86, 6, 061109 (2012).Google Scholar
Merton, R. C., Theory of rational option pricing. The Bell Journal of Economics and Management Science, 4, 1, 141 (1973).Google Scholar
Metz, F. L., Neri, I., and Rogers, T., Spectral theory of sparse non-Hermitian random matrices, Journal of Physics A: Mathematical and Theoretical, 52, 43, 434003 (2019).Google Scholar
Miller, A. and Abrahams, E., Impurity conduction at low concentrations, Physical Review, 120, 3, 745 (1960).Google Scholar
Mlodinow, L., The Drunkard’s Walk: How Randomness Rules Our Lives, Vintage (2009).Google Scholar
Möbius, W., Neher, R. A., and Gerland, U., Kinetic accessibility of buried DNA sites in nucleosomes, Physical Review Letters, 97, 20, 208102 (2006).Google Scholar
Montroll, E. W. and Shlesinger, M. F., On the wedding of certain dynamical processes in disordered complex materials to the theory of stable (Levy) distribution functions, in: The Mathematics and Physics of Disordered Media: Percolation, Random Walk, Modeling, and Simulation, pp. 109–137, Springer, Berlin, Heidelberg (1983).Google Scholar
Morin, D. J., Probability: For the Enthusiastic Beginner, Createspace Independent Publishing Platform (2016).Google Scholar
Mott, N. F., Conduction in non-crystalline materials: III. Localized states in a pseudogap and near extremities of conduction and valence bands, Philosophical Magazine, 19, 160, 835 (1969).Google Scholar
Muskhelishvili, N. I. and Radok, J. R. M., Singular Integral Equations: Boundary Problems of Function Theory and Their Application to Mathematical Physics, Courier Corporation (2008).Google Scholar
Nesbitt, J. R. and Hebard, A. F., Time-dependent glassy behavior of interface states in Al- Al Ox - Al tunnel junctions, Physical Review B, 75, 19, 195441 (2007).Google Scholar
Newman, M., Networks: An Introduction, 2nd edn, Oxford University Press (2018).Google Scholar
Orlyanchik, V. and Ovadyahu, Z., Stress aging in the electron glass, Physical Review Letters, 92, 6, 066801 (2004).Google Scholar
Orr, H. A., The distribution of fitness effects among beneficial mutations. Genetics, 163(4), pp. 15191526 (2003).Google Scholar
Page, L. et al., The PageRank Citation Ranking: Bringing Order to the Web, Technical Report, Stanford InfoLab, Stanford, California (1999).Google Scholar
Paul, W. and Baschnagel, J., Stochastic Processes, Springer (2013).Google Scholar
Pearle, P., Collett, B., Bart, K., Bilderback, D., Newman, D., and Samuels, S., What Brown saw and you can too, American Journal of Physics, 78, 12, 1278 (2010).Google Scholar
Pearson, K., The problem of the random walk, Nature, 72, 1865, 294 (1905).Google Scholar
Perrin, J., Brownian Movement and Molecular Reality, Courier Corporation (2013).Google Scholar
Pinski, G. and Narin, F., Citation influence for journal aggregates of scientific publications: Theory, with application to the literature of physics, Information Processing and Management, 12, 5, 297 (1976).Google Scholar
Porat, B., Digital Processing of Random Signals: Theory and Methods. Courier Dover Publications (2008).Google Scholar
Pugatch, R. et al., Anomalous symmetry breaking in classical two-dimensional diffusion of coherent atoms, Physical Review A, 89, 3, 033807 (2014).Google Scholar
Qazilbash, M. M. et al., Mott transition in VO2 revealed by infrared spectroscopy and nano-imaging, Science, 318, 5857,1750 (2007).Google Scholar
Redner, S., A Guide to First-Passage Processes. Cambridge University Press (2001).Google Scholar
Reznikov, M., De Picciotto, R., Griffiths, T. G., Heiblum, M., and Umansky, V., Observation of quasiparticles with one-fifth of an electron’s charge, Nature, 399, 6733, 238 (1999).Google Scholar
Robert, L. et al., Division in Escherichia coli is triggered by a size-sensing rather than a timing mechanism, BMC biology 12, 1, 17 (2014).Google Scholar
Roos, M., Böcking, D., Gyimah, K. O., Kucerova, G., Bansmann, J., Biskupek, J., Kaiser, U., Hüsing, N., and Behm, R. J., Nanostructured, mesoporous Au/TiO2 model catalysts– structure, stability and catalytic properties, Beilstein Journal of Nanotechnology, 2, 1, 593 (2011).Google Scholar
Rosenzweig, N. and Porter, C. E., Repulsion of energy levels in complex atomic spectra, Physical Review, 120, 5, 1698 (1960).Google Scholar
Ruderman, D. L. and Bialek, W., Statistics of natural images: Scaling in the woods, in: Advances in Neural Information Processing Systems, pp. 551–558 (1994).Google Scholar
Scher, H. and Montroll, E. W., Anomalous transit-time dispersion in amorphous solids, Physical Review B, 12, 6, 2455 (1975).Google Scholar
Schey, H. M. and Schey, H. M., Div, Grad, Curl, and All That: An Informal Text on Vector Calculus, New York: WW Norton (2005).Google Scholar
Schuss, Z., Theory and Applications of Stochastic Processes: An Analytical Approach, Springer Science and Business Media (2009).Google Scholar
Sethna, J., Statistical Mechanics: Entropy, Order Parameters, and Complexity. Oxford University Press (2006).Google Scholar
Shklovskii, B. I. and Efros, A. L., Electronic Properties of Doped Semiconductors, Springer Science and Business Media (2013).Google Scholar
Shockley, W., On the statistics of individual variations of productivity in research laboratories, Proceedings of the IRE, 45, 3, 279 (1957).Google Scholar
Soifer, I., Robert, L., and Amir, A., Single-cell analysis of growth in budding yeast and bacteria reveals a common size regulation strategy, Current Biology, 26, 3, 356 (2016).Google Scholar
Sommers, H. J. et al., Spectrum of large random asymmetric matrices, Physical Review Letters 60, 19, 1895 (1988).Google Scholar
Sornette, D., Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools, Springer Science and Business Media (2006).Google Scholar
Stauffer, D. and Aharony, A., Introduction to Percolation Theory, CRC press, 1994.Google Scholar
Stein, E. M. and Shakarchi, R., Complex Analysis (Vol. 2), Princeton University Press (2010).Google Scholar
Strogatz, S. H., Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry, and Engineering, CRC Press (2018).Google Scholar
Suzuki, Y. and Dudko, O. K., Single-molecule rupture dynamics on multidimensional landscapes, Physical Review Letters, 104, 4, 048101 (2010).Google Scholar
Taleb, N. N., The Black Swan: The Impact of the Highly Improbable, Random House (2007).Google Scholar
Theis, C. V., The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using ground water storage, Washington, DC: US Department of the Interior, Geological Survey, Water Resources Division, Ground Water Branch, 5 (1935).Google Scholar
Touchette, H., The large deviation approach to statistical mechanics, Physics Reports, 478, 1–3, 1 (2009).Google Scholar
Tracy, C. A. and Widom, H., Level-spacing distributions and the Airy kernel, Communications in Mathematical Physics, 159, 1, 151 (1994).Google Scholar
Tricomi, F. G., Integral Equations, Courier Corporation (1985).Google Scholar
Van Kampen, N. G., Stochastic Processes in Physics and Chemistry, Elsevier (1992).Google Scholar
Vezzani, A., Barkai, E., and Burioni, R., Single-big-jump principle in physical modeling, Physical Review E, 100, 1, 012108 (2019).Google Scholar
Vivo, P., Large deviations of the maximum of independent and identically distributed random variables, European Journal of Physics, 36, 5, 055037 (2015).CrossRefGoogle Scholar
Walley, P. A. and Jonscher, A. K., Electrical conduction in amorphous germanium, Thin Solid Films, 1, 5,367 (1968).Google Scholar
Wang, W., Vezzani, A., Burioni, R., and Barkai, E., Transport in disordered systems: the single big jump approach, Physical Review Research, 1, 3, 033172 (2019).Google Scholar
Wigner, E. P., Characteristic vectors of bordered matrices with infinite dimensions, Annals of Mathematics, 62, 3, 548 (1955).Google Scholar
Wigner, E. P., Statistical properties of real symmetric matrices with many dimensions, in: Proceedings of the Canadian Mathematical Congress, University of Toronto, pp. 174–184, (1957).Google Scholar
Williams, M., The missing curriculum in physics problem-solving education, Science and Education, 27, 3-4, 299 (2018).Google Scholar
Ziff, R. M. and Newman, M. E. J., Convergence of threshold estimates for two-dimensional percolation, Physical Review E, 66, 1, 016129 (2002).Google Scholar

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  • References
  • Ariel Amir, Harvard University, Massachusetts
  • Book: Thinking Probabilistically
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  • Book: Thinking Probabilistically
  • Online publication: 15 December 2020
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