Subdiffusive heat-kernel decay in four-dimensional i.i.d. random conductance models

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12510%2F12%3A43884532" target="_blank" >RIV/60076658:12510/12:43884532 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Subdiffusive heat-kernel decay in four-dimensional i.i.d. random conductance models

Popis výsledku v původním jazyce

We study the diagonal heat-kernel decay for the four-dimensional nearest-neighbor random walk among i.i.d. random conductances that are positive, bounded from above but can have arbitrarily heavy tails at zero. It has been known that the quenched returnprobability after 2n steps is at most a constant times n^{-2} log(n), but the best lower bound till now has been a constant times n^{-2}. Here we will show that the log(n) term marks a real phenomenon by constructing an environment, for each sequence lambda_n tending to infinity, such that the heat kernel is at least Cn^{-2} log(n)/lambda_n, with C}0 almost surely, along a deterministic subsequence of n's. Notably, this holds simultaneously with a (non-degenerate) quenched invariance principle. As for dimensions 5 and above studied earlier, the source of the anomalous decay is a trapping phenomenon although the contribution is in this case collected from a whole range of spatial scales.

Název v anglickém jazyce

Subdiffusive heat-kernel decay in four-dimensional i.i.d. random conductance models

Popis výsledku anglicky

We study the diagonal heat-kernel decay for the four-dimensional nearest-neighbor random walk among i.i.d. random conductances that are positive, bounded from above but can have arbitrarily heavy tails at zero. It has been known that the quenched returnprobability after 2n steps is at most a constant times n^{-2} log(n), but the best lower bound till now has been a constant times n^{-2}. Here we will show that the log(n) term marks a real phenomenon by constructing an environment, for each sequence lambda_n tending to infinity, such that the heat kernel is at least Cn^{-2} log(n)/lambda_n, with C}0 almost surely, along a deterministic subsequence of n's. Notably, this holds simultaneously with a (non-degenerate) quenched invariance principle. As for dimensions 5 and above studied earlier, the source of the anomalous decay is a trapping phenomenon although the contribution is in this case collected from a whole range of spatial scales.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BE - Teoretická fyzika

OECD FORD obor

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Projekt

<a href="/cs/project/GAP201%2F11%2F1558" target="_blank" >GAP201/11/1558: Náhodné procházky a náhodná pole v modelech statistické fyziky</a><br>

Návaznosti

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

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

Journal of the London Mathematical Society

ISSN

1469-7750

e-ISSN

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Svazek periodika

86

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

28

Strana od-do

455-481

Kód UT WoS článku

000309465500007

EID výsledku v databázi Scopus

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