C. Boldrighini

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Articles: 1

Weak dependence for a class of local functionals of Markov chains on ${\mathbb Z}^d$

C. Boldrighini, A. Marchesiello, C. Saffirio

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 21 (2015), no. 4, 302-314

In many models of Mathematical Physics, based on the study of a Markov chain $\widehat \eta= \{\eta_{t}\}_{t=0}^{\infty}$ on ${\mathbb Z}^d$, one can prove by perturbative arguments a contraction property of the stochastic operator restricted to a subspace of local functions $\mathcal H_{M}$ endowed with a suitable norm. We show, on the example of a model of random walk in random environment with mutual interaction, that the condition is enough to prove a Central Limit Theorem for sequences $\{f(S^{k}\widehat \eta)\}_{k=0}^{\infty}$, where $S$ is the time shift and $f$ is strictly local in space and belongs to a class of functionals related to the H\"older continuous functions on the torus $T^{1}$.

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