Mathematics

Dr. Nishant Chandgotia
Tel Aviv University

In 1970, Krieger proved that any free ergodic probability preserving invertible transformation of finite entropy can be modeled by A^Z, the set of unconstrained bi-infinite sequences in some finite alphabet A. This result has seen many generalisations for more constrained systems and for actions of other groups. Along with Tom Meyerovitch, we prove that under certain general mixing conditions $Z^d$-topological dynamical systems can model all free ergodic probability preserving Z^d actions of lower entropy. In particular, we show that these mixing conditions are satisfied by proper colourings of the Z^d lattice (colourings of the Z^d lattice where adjacent colours are distinct) and the domino tilings of Z^2 lattice, thus answering a question by Şahin and Robinson. The talk will begin with an introduction to the terms mentioned in the abstract and should be accessible to a general audience.