Return Probability and Recurrence for the Random Walk Driven by Two-Dimensional Gaussian Free Field

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11620%2F20%3A10491821" target="_blank" >RIV/00216208:11620/20:10491821 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=92ixnNnRVG" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=92ixnNnRVG</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00220-019-03589-z" target="_blank" >10.1007/s00220-019-03589-z</a>

Result language
angličtina
Original language name
Return Probability and Recurrence for the Random Walk Driven by Two-Dimensional Gaussian Free Field
Original language description
Given any gamma>0 and for eta={eta(v)}(v is an element of Z2) denoting a sample of the two-dimensional discrete Gaussian free field on Z(2) pinned at the origin, we consider the random walk on Z(2) among random conductances where the conductance of edge (u, v) is given by e(gamma) (eta(u) + eta(v)). We show that, for almost every eta, this random walk is recurrent and that, with probability tending to 1 as T -> infinity, the return probability at time 2T decays as T-1+o(1). In addition, we prove a version of subdiffusive behavior by showing that the expected exit time from a ball of radius N scales as N psi(gamma)+o(1) with psi(gamma) > 2 for all gamma > 0. Our results rely on delicate control of the effective resistance for this random network. In particular, we show that the effective resistance between two vertices at Euclidean distance N behaves as N-o(1).
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10103 - Statistics and probability

Project
<a href="/en/project/GA16-15238S" target="_blank" >GA16-15238S: Collective behavior of large stochastic systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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