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Equivariant thinning over a free group

Part of: Stochastic processes Distribution theory - Probability Ergodic theory

Published online by Cambridge University Press:  25 September 2018

TERRY SOO  and
AMANDA WILKENS Open the ORCID record for AMANDA WILKENS [Opens in a new window]
TERRY SOO
Affiliation:
Department of Mathematics, University of Kansas, 405 Snow Hall, 1460 Jayhawk Blvd, Lawrence, Kansas 66045-7594, USA email tsoo@ku.edu, awilkens@ku.edu
AMANDA WILKENS
Affiliation:
Department of Mathematics, University of Kansas, 405 Snow Hall, 1460 Jayhawk Blvd, Lawrence, Kansas 66045-7594, USA email tsoo@ku.edu, awilkens@ku.edu
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Abstract

We construct entropy increasing monotone factors in the context of a Bernoulli shift over the free group of rank at least two.

Keywords

Sinai factor theoremOrnstein and Weissthinningmonotone couplingnon-amenable group

MSC classification

Primary: 37A35: Entropy and other invariants, isomorphism, classification
Secondary: 60G10: Stationary processes 60E15: Inequalities; stochastic orderings
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 4 , April 2020 , pp. 1057 - 1067
Copyright
© Cambridge University Press, 2018

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References

Angel, O., Holroyd, A. E. and Soo, T.. Deterministic thinning of finite Poisson processes. Proc. Amer. Math. Soc. 139(2) (2011), 707–720.Google Scholar
Ball, K.. Factors of independent and identically distributed processes with non-amenable group actions. Ergod. Th. & Dynam. Sys. 25(3) (2005), 711–730.Google Scholar
Ball, K.. Monotone factors of i.i.d. processes. Israel J. Math. 150(1) (2005), 205–227.Google Scholar
Ball, K.. Poisson thinning by monotone factors. Electron. Commun. Probab. 10 (2005), 60–69 (electronic).Google Scholar
Bowen, L. P.. A measure-conjugacy invariant for free group actions. Ann. of Math. (2) 171(2) (2010), 1387–1400.Google Scholar
Gurel-Gurevich, O. and Peled, R.. Poisson thickening. Israel J. Math. 196(1) (2013), 215–234.Google Scholar
Holroyd, A. E., Lyons, R. and Soo, T.. Poisson splitting by factors. Ann. Probab. 39(5) (2011), 1938–1982.Google Scholar
Katok, A.. Fifty years of entropy in dynamics: 1958–2007. J. Mod. Dyn. 1(4) (2007), 545–596.Google Scholar
Keane, M. and Smorodinsky, M.. A class of finitary codes. Israel J. Math. 26 (1977), 352–371.Google Scholar
Keane, M. and Smorodinsky, M.. Bernoulli schemes of the same entropy are finitarily isomorphic. Ann. of Math. (2) 109 (1979), 397–406.Google Scholar
Lyons, R.. Factors of IID on trees. Combin. Probab. Comput. 26(2) (2017), 285–300.Google Scholar
Ornstein, D.. Bernoulli shifts with the same entropy are isomorphic. Adv. Math. 4(3) (1970), 337–352.Google Scholar
Ornstein, D. S. and Weiss, B.. Entropy and isomorphism theorems for actions of amenable groups. J. Anal. Math. 48(1) (1987), 1–141.Google Scholar
Quas, A. and Soo, T.. A monotone Sinai theorem. Ann. Probab. 44(1) (2016), 107–130.Google Scholar
Sinai, Y. G.. Selecta (Ergodic Theory and Dynamical Systems). Vol. I. Springer, New York, 2010.Google Scholar
Soo, T.. A monotone isomorphism theorem. Probab. Theory Related Fields 167(3–4) (2017), 1117–1136.Google Scholar
Srivastava, S. M.. A Course on Borel Sets (Graduate Texts in Mathematics, 180). Springer, New York, 1998.Google Scholar
Strassen, V.. The existence of probability measures with given marginals. Ann. Math. Statist. 36(2) (1965), 423–439.Google Scholar
Weiss, B.. The isomorphism problem in ergodic theory. Bull. Amer. Math. Soc. (N.S.) 78(5) (1972), 668–684.Google Scholar