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

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 $.

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