Around Tsirelson's equation, or: The evolution process may not explain everything

TL;DR

This paper reviews developments related to Tsirelson's equation, focusing on Markov chains in compact groups, especially the one-dimensional torus, highlighting that evolution processes may not fully explain certain phenomena.

Contribution

It synthesizes recent advances around Tsirelson's equation in the context of Markov chains on compact groups, emphasizing the limitations of evolution processes.

Findings

Analysis of Tsirelson's equation in compact groups

Detailed discussion of the one-dimensional torus case

Illustration of evolution process limitations

Abstract

We present a synthesis of a number of developments which have been made around the celebrated Tsirelson's equation (1975), conveniently modified in the framework of a Markov chain taking values in a compact group $ G $, and indexed by negative time. To illustrate, we discuss in detail the case of the one-dimensional torus $ G=\bT $.