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
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DOI - Digital Object Identifier
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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
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Result continuities
Project
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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
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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
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UT code for WoS article
000256203800010
EID of the result in the Scopus database
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