The authors consider a random walk on Z in a random environment independent in space and with a Markov evolution in time (an ergodic Markov chain with finitely many states). They study the annealed correlations of the jumps, or the time correlations of the "field from the point of view of the random walk''. The authors prove that for small stochasticity the time correlation behaves as t to the power -1/2 multiplied by exp(-t alpha1), for alpha1>0. The analysis shows that, as the parameters of the model vary, a transition to a fall-off of the type exp(-t alpha), for alpha∈(0,alpha1), may occur.
Asymptotic decay of correlations for a Random walk in interaction with a Markov field / Boldrighini, C.; Minlos, R. A.; Nardi, F. R.; Pellegrinotti A.. - In: MOSCOW MATHEMATICAL JOURNAL. - ISSN 1609-3321. - STAMPA. - 5:(2005), pp. 507-522. [10.17323/1609-4514-2005-5-3-507-522]
Asymptotic decay of correlations for a Random walk in interaction with a Markov field
NARDI, FRANCESCA ROMANA;
2005
Abstract
The authors consider a random walk on Z in a random environment independent in space and with a Markov evolution in time (an ergodic Markov chain with finitely many states). They study the annealed correlations of the jumps, or the time correlations of the "field from the point of view of the random walk''. The authors prove that for small stochasticity the time correlation behaves as t to the power -1/2 multiplied by exp(-t alpha1), for alpha1>0. The analysis shows that, as the parameters of the model vary, a transition to a fall-off of the type exp(-t alpha), for alpha∈(0,alpha1), may occur.File | Dimensione | Formato | |
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