Título: Probabilistic cellular automata with Bernoulli invariant measures

Palestrante: Siamak Taati (American University of Beirut)
Data: 24/01/2022
Horário: 15hrs
Local: Transmissão online

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Resumo: I will sketch a proof of the following result: If a positive-rate probabilistic cellular automaton has a Bernoulli invariant measure, then it is ergodic, meaning that its distribution starting from any configuration converges (exponentially fast) to that Bernoulli measure. The same result holds for (continuous-time) interacting particle systems. The proof is based on the entropy method, but unlike the usual entropy arguments, does not require the shift-invariance of the starting measure. This result has a practical implication concerning the inevitability of heat dissipation in computers which I will briefly discuss. This is a joint work with Irène Marcovici.

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Organizers: Giulio Iacobelli and Maria Eulalia Vares