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

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 $G=\mathbb{T}$.