Skip to main content Accessibility help
×
Home

Equivariant thinning over a free group

  • TERRY SOO (a1) and AMANDA WILKENS (a1)

Abstract

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

Copyright

References

Hide All
[1]Angel, O., Holroyd, A. E. and Soo, T.. Deterministic thinning of finite Poisson processes. Proc. Amer. Math. Soc. 139(2) (2011), 707720.
[2]Ball, K.. Factors of independent and identically distributed processes with non-amenable group actions. Ergod. Th. & Dynam. Sys. 25(3) (2005), 711730.
[3]Ball, K.. Monotone factors of i.i.d. processes. Israel J. Math. 150(1) (2005), 205227.
[4]Ball, K.. Poisson thinning by monotone factors. Electron. Commun. Probab. 10 (2005), 6069 (electronic).
[5]Bowen, L. P.. A measure-conjugacy invariant for free group actions. Ann. of Math. (2) 171(2) (2010), 13871400.
[6]Gurel-Gurevich, O. and Peled, R.. Poisson thickening. Israel J. Math. 196(1) (2013), 215234.
[7]Holroyd, A. E., Lyons, R. and Soo, T.. Poisson splitting by factors. Ann. Probab. 39(5) (2011), 19381982.
[8]Katok, A.. Fifty years of entropy in dynamics: 1958–2007. J. Mod. Dyn. 1(4) (2007), 545596.
[9]Keane, M. and Smorodinsky, M.. A class of finitary codes. Israel J. Math. 26 (1977), 352371.
[10]Keane, M. and Smorodinsky, M.. Bernoulli schemes of the same entropy are finitarily isomorphic. Ann. of Math. (2) 109 (1979), 397406.
[11]Lyons, R.. Factors of IID on trees. Combin. Probab. Comput. 26(2) (2017), 285300.
[12]Ornstein, D.. Bernoulli shifts with the same entropy are isomorphic. Adv. Math. 4(3) (1970), 337352.
[13]Ornstein, D. S. and Weiss, B.. Entropy and isomorphism theorems for actions of amenable groups. J. Anal. Math. 48(1) (1987), 1141.
[14]Quas, A. and Soo, T.. A monotone Sinai theorem. Ann. Probab. 44(1) (2016), 107130.
[15]Sinai, Y. G.. Selecta (Ergodic Theory and Dynamical Systems). Vol. I. Springer, New York, 2010.
[16]Soo, T.. A monotone isomorphism theorem. Probab. Theory Related Fields 167(3–4) (2017), 11171136.
[17]Srivastava, S. M.. A Course on Borel Sets (Graduate Texts in Mathematics, 180). Springer, New York, 1998.
[18]Strassen, V.. The existence of probability measures with given marginals. Ann. Math. Statist. 36(2) (1965), 423439.
[19]Weiss, B.. The isomorphism problem in ergodic theory. Bull. Amer. Math. Soc. (N.S.) 78(5) (1972), 668684.

Keywords

MSC classification

Equivariant thinning over a free group

  • TERRY SOO (a1) and AMANDA WILKENS (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.