Dynamical intricacy and average sample complexity of amenable group actions

[1]  L. Bowen.  A BRIEF INTRODUCTION TO SOFIC ENTROPY THEORY , 2017, Proceedings of the International Congress of Mathematicians (ICM 2018).

[2]  Ruifeng Zhang,et al.  A note on dimensional entropy for amenable group actions , 2017, 1712.06152.

[3]  L. Zambotti,et al.  Mean mutual information and symmetry breaking for finite random fields , 2012 .

[4]  Wen Huang,et al.  Measure complexity and Möbius disjointness , 2017, Advances in Mathematics.

[5]  Jean Moulin Ollagnier,et al.  Ergodic Theory and Statistical Mechanics , 1985 .

[6]  Misha Gromov,et al.  Topological Invariants of Dynamical Systems and Spaces of Holomorphic Maps: I , 1999 .

[7]  Edward T. Bullmore,et al.  Fundamentals of Brain Network Analysis , 2016 .

[8]  Yun Zhao.  Measure-theoretic pressure for amenable group actions , 2017 .

[9]  G. Edelman,et al.  A measure for brain complexity: relating functional segregation and integration in the nervous system. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[10]  R. Bowen.  TOPOLOGICAL ENTROPY FOR NONCOMPACT SETS , 1973 .

[11]  Benjamin Weiss,et al.  Ergodic theory of amenable group actions. I: The Rohlin lemma , 1980 .

[12]  Ercai Chen,et al.  Bowen entropy for actions of amenable groups , 2014, 1410.4645.

[13]  L. Zambotti,et al.  Approximate maximizers of intricacy functionals , 2009, Probability Theory and Related Fields.

[14]  V. Rokhlin.  LECTURES ON THE ENTROPY THEORY OF MEASURE-PRESERVING TRANSFORMATIONS , 1967 .

[15]  Benjamin Weiss,et al.  Entropy and isomorphism theorems for actions of amenable groups , 1987 .

[16]  K. Petersen,et al.  Dynamical intricacy and average sample complexity , 2015, 1512.01143.

[17]  T. Downarowicz,et al.  Tilings of amenable groups , 2015, Journal für die reine und angewandte Mathematik (Crelles Journal).

[18]  Simon B Eickhoff,et al.  Imaging-based parcellations of the human brain , 2018, Nature Reviews Neuroscience.

[19]  Benjamin Weiss,et al.  Mean topological dimension , 2000 .