Localization of the principal Dirichlet eigenvector in the heavy-tailed random conductance model
dc.bibliographicCitation.firstPage | 68 | eng |
dc.bibliographicCitation.journalTitle | Electronic journal of probability : EJP | eng |
dc.bibliographicCitation.volume | 23 | eng |
dc.contributor.author | Flegel, Franziska | |
dc.date.accessioned | 2022-06-21T12:07:35Z | |
dc.date.available | 2022-06-21T12:07:35Z | |
dc.date.issued | 2018 | |
dc.description.abstract | We study the asymptotic behavior of the principal eigenvector and eigenvalue of the random conductance Laplacian in a large domain of Zd (d≥2) with zero Dirichlet condition. We assume that the conductances w are positive i.i.d. random variables, which fulfill certain regularity assumptions near zero. If γ=sup{q≥0:E[w−q]<∞}<1/4, then we show that for almost every environment the principal Dirichlet eigenvector asymptotically concentrates in a single site and the corresponding eigenvalue scales subdiffusively. The threshold γc=1/4 is sharp. Indeed, other recent results imply that for γ>1/4 the top of the Dirichlet spectrum homogenizes. Our proofs are based on a spatial extreme value analysis of the local speed measure, Borel-Cantelli arguments, the Rayleigh-Ritz formula, results from percolation theory, and path arguments. | eng |
dc.description.version | publishedVersion | eng |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/9100 | |
dc.identifier.uri | https://doi.org/10.34657/8138 | |
dc.language.iso | eng | eng |
dc.publisher | [Madralin] : EMIS ELibEMS | eng |
dc.relation.doi | https://doi.org/10.1214/18-EJP160 | |
dc.relation.essn | 1083-6489 | |
dc.rights.license | CC BY 4.0 Unported | eng |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | eng |
dc.subject.ddc | 510 | eng |
dc.subject.other | Borel-Cantelli | eng |
dc.subject.other | Dirichlet spectrum | eng |
dc.subject.other | Extreme value analysis | eng |
dc.subject.other | Path arguments | eng |
dc.subject.other | Percolation | eng |
dc.subject.other | Random conductance model | eng |
dc.subject.other | Random walk | eng |
dc.subject.other | Variational formula | eng |
dc.title | Localization of the principal Dirichlet eigenvector in the heavy-tailed random conductance model | eng |
dc.type | Article | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Zeitschriftenartikel | eng |
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