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A class of random walks in reversible dynamic environment: antisymmetry and applications to the East model | | Luca Avena
; Oriane Blondel
; Alessandra Faggionato
; | | Date: |
16 May 2016 | | Abstract: | We introduce via perturbation a class of random walks in reversible dynamic
environments having a spectral gap. In this setting one can apply the
mathematical results derived in this http URL As first
results, we show that the asymptotic velocity is antisymmetric in the
perturbative parameter and, for a subclass of random walks, we characterize the
velocity and a stationary distribution of the environment seen from the walker
as suitable series in the perturbative parameter. We then consider as a special
case a random walk on the East model that tends to follow dynamical interfaces
between empty and occupied regions. We study the asymptotic velocity and
density profile for the environment seen from the walker. In particular, we
determine the sign of the velocity when the density of the underlying East
process is not 1/2, and we discuss the appearance of a drift in the balanced
setting given by density 1/2. | | Source: | arXiv, 1605.4816 | | Services: | Forum | Review | PDF | Favorites | |
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