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

Result code in 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>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Subdiffusive heat-kernel decay in four-dimensional i.i.d. random conductance models
Original language description
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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Project
<a href="/en/project/GAP201%2F11%2F1558" target="_blank" >GAP201/11/1558: Random walks and random fields in models of statistical mechanics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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