C. Boldrighini
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Weak dependence for a class of local functionals of Markov chains on Zd
C. Boldrighini, A. Marchesiello, C. Saffirio
MFAT 21 (2015), no. 4, 302-314
302-314
In many models of Mathematical Physics, based on the study of a Markov chain ˆη={ηt}∞t=0 on Zd, one can prove by perturbative arguments a contraction property of the stochastic operator restricted to a subspace of local functions HM 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(Skˆη)}∞k=0, 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 T1.