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Hitting spheres by straight-line motion or Brownian motion

Published online by Cambridge University Press:  14 July 2016

E. G. Enns ,
B. R. Smith  and
P. F. Ehlers
E. G. Enns*
Affiliation:
University of Calgary
B. R. Smith*
Affiliation:
University of Calgary
P. F. Ehlers*
Affiliation:
University of Calgary
*
∗ Postal address: Department of Mathematics and Statistics, Faculty of Science, The University of Calgary, 2500 University Drive N.W., Calgary, Alberta, Canada T2N 1N4.
∗ Postal address: Department of Mathematics and Statistics, Faculty of Science, The University of Calgary, 2500 University Drive N.W., Calgary, Alberta, Canada T2N 1N4.
∗ Postal address: Department of Mathematics and Statistics, Faculty of Science, The University of Calgary, 2500 University Drive N.W., Calgary, Alberta, Canada T2N 1N4.
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Abstract

Points randomly placed in Rn are independently assigned a speed and direction of motion. The time between collisions with a central n-sphere is obtained. If instead of straight-line motion the points perform Brownian motion, the analogous inter-collision-time distribution is obtained.

Keywords

FIRST-PASSAGE TIME
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 1 , March 1984 , pp. 70 - 79
Copyright
Copyright © Applied Probability Trust 1984 

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References

Dobrushin, R. L. (1956) On Poisson laws of distributions of particles in space. Ukrain. Mat. Zurn. 8, 127–134.Google Scholar
Gradshteyn, I. S. and Ryzik, I. M. (1965) Table of Integrals, Series, and Products. Academic Press, New York.Google Scholar
Jaegar, J. C. (1943) Heat flow in a region bounded internally by a circular cylinder. Proc. R. Soc. Edinburgh A61, 223–230.Google Scholar
Kallenberg, O. (1978) On the independence of velocities in a system of noninteracting particles. Ann. Prob. 6, 885–890.CrossRefGoogle Scholar
Lukacs, E. (1960) Characteristic Functions. Griffin, London.Google Scholar
Naqui, K. R. (1974) Diffusion controlled reactions in two-dimensional fluids: discussion of measurements of lateral diffusion of lipids in biological membranes. Chem. Phys. Letters 28, 280–284.Google Scholar
Papangelou, F. (1980) On the convergence of interacting particle systems to the Poisson process. Z. Wahrscheinlichkeitsth. 52, 235–249.CrossRefGoogle Scholar
Spitzer, F. (1958) Some theorems concerning 2-dimensional Brownian motion. Trans. Amer. Math. Soc. 87, 187–197.CrossRefGoogle Scholar
Thedeen, T. (1967) Convergence and invariance questions for point systems in R1 under random motion. Ark. Mat. 7, 211–239.CrossRefGoogle Scholar
Wendel, J. G. (1980) Hitting spheres with Brownian motion. Ann. Prob. 8, 164–169.CrossRefGoogle Scholar