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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

Given any gamma&gt;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 -&gt; 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) &gt; 2 for all gamma &gt; 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).

Název v anglickém jazyce

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

Popis výsledku anglicky

Given any gamma&gt;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 -&gt; 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) &gt; 2 for all gamma &gt; 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).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GA16-15238S" target="_blank" >GA16-15238S: Kolektivní chování velkých stochastických systémů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Communications in Mathematical Physics

ISSN

0010-3616

e-ISSN

1432-0916

Svazek periodika

373

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

VG - Britské Panenské ostrovy

Počet stran výsledku

62

Strana od-do

45-106

Kód UT WoS článku

000514316600002

EID výsledku v databázi Scopus

2-s2.0-85075875088