Invariance principle for the random conductance model

We study a continuous time random walk X in an environment of i.i.d. random conductances in . We assume that , so that the bonds with strictly positive conductances percolate, but make no other assumptions on the law of the μ e . We prove a quenched invariance principle for X , and obtain Green’s f...

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Veröffentlicht in:	Probability theory and related fields 2013-08, Vol.156 (3-4), p.535-580
Hauptverfasser:	Andres, S., Barlow, M. T., Deuschel, J.-D., Hambly, B. M.
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Brownian motion Conductance Economics Finance Green's functions Heat Heat conductivity Inequalities Insurance Invariance Law Management Mathematical and Computational Biology Mathematical and Computational Physics Mathematical models Mathematics Mathematics and Statistics Operations Research/Decision Theory Probability Probability theory Probability Theory and Stochastic Processes Quantitative Finance Quenching (cooling) Random variables Random walk Statistics for Business Studies Theorems Theoretical
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Beschreibung
Zusammenfassung:	We study a continuous time random walk X in an environment of i.i.d. random conductances in . We assume that , so that the bonds with strictly positive conductances percolate, but make no other assumptions on the law of the μ e . We prove a quenched invariance principle for X , and obtain Green’s functions bounds and an elliptic Harnack inequality.
ISSN:	0178-8051 1432-2064
DOI:	10.1007/s00440-012-0435-2