Sandro Gallo

Attractive regular stochastic chains: perfect simulation and phase transition

We prove that uniqueness of the stationary chain, or equivalently, of the

Rumor processes on

g

\N

-measure, compatible with an attractive regular probability kernel is equivalent to either one of the following two assertions for this chain: (1) it is a finitary coding of an i.i.d. process with countable alphabet, (2) the concentration of measure holds at exponential rate. We show in particular that if a stationary chain is uniquely defined by a kernel that is continuous and attractive, then this chain can be sampled using a coupling-from-the-past algorithm. For the original Bramson-Kalikow model we further prove that there exists a unique compatible chain if and only if the chain is a finitary coding of a finite alphabet i.i.d. process. Finally, we obtain some partial results on conditions for phase transition for general chains of infinite order.

and discrete renewal processes

We study two rumor processes on

Perfect Simulation and Convex Mixture of Context Trees

mathbb {N}

The Shortest Possible Return Time of

N, the dynamics of which are related to an SI epidemic model with long range transmission. Both models start with one spreader at site

-Mixing Processes

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