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Anomalous heat-kernel decay for random walk among bounded random conductances

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12510%2F08%3A00009443" target="_blank" >RIV/60076658:12510/08:00009443 - isvavai.cz</a>

  • Result on the web

  • DOI - Digital Object Identifier

Alternative languages

  • Result language

    angličtina

  • Original language name

    Anomalous heat-kernel decay for random walk among bounded random conductances

  • Original language description

    We consider the nearest-neighbor simple random walk on Z(d), d >= 2, driven by a field of bounded random conductances omega(xy) is an element of [0, 1]. The conductance law is i.i.d. subject to the condition that the probability of omega(xy) > 0 exceedsthe threshold for bond percolation on Z(d). For environments in which the origin is connected to infinity by bonds with positive conductances, we study the decay of the 2n-step return probability P-omega(2n) (0, 0). We prove that P-omega(2n) (0, 0) is bounded by a random constant times n(-d/2) in d = 2, 3, while it is o(n(-2)) in d >= 5 and O(n(-2) log n) in d = 4. By producing examples with anomalous heat-kernel decay approaching 1/n(2), we prove that the o(n(-2)) bound in d >= 5 is the best possible.We also construct natural n-dependent environments that exhibit the extra log n factor in d = 4.

  • Czech name

    Neobvyklý útlum tepelného jádra při náhodné procházce mezi náhodně omezujícími podmínkami tepelné vodivosti.

  • Czech description

    Uvažujeme nejbližší sousední jednoduchou náhodnou procházku na Z(d), d >= 2 vedenou polem náhodných omezujících vodivostí omega(xy), který je prvkem [0, 1]. V článku konstruujeme přírodní n-prvkové prostředí s extra dlouhým logaritmickým dělitelem pro d=4.

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BB - Applied statistics, operational research

  • OECD FORD branch

Result continuities

  • Project

  • Continuities

    V - Vyzkumna aktivita podporovana z jinych verejnych zdroju

Others

  • Publication year

    2008

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES

  • ISSN

    0246-0203

  • e-ISSN

  • Volume of the periodical

    274

  • Issue of the periodical within the volume

    2

  • Country of publishing house

    FI - FINLAND

  • Number of pages

    19

  • Pages from-to

  • UT code for WoS article

    000256203800010

  • EID of the result in the Scopus database