Electronic Journal of Probability

Standard Spectral Dimension for the Polynomial Lower Tail Random Conductances Model

Omar Boukhadra

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Abstract

We study models of continuous-time, symmetric random walks in random environment on the d-dimensional integer lattice, driven by a field of i.i.d random nearest-neighbor conductances bounded only from above with a power law tail near 0. We are interested in estimating the quenched asymptotic behavior of the on-diagonal heat-kernel. We show that the spectral dimension is standard when we lighten sufficiently the tails of the conductances. As an expected consequence, the same result holds for the discrete-time case.

Article information

Source
Electron. J. Probab., Volume 15 (2010), paper no. 68, 2069-2086.

Dates
Accepted: 8 December 2010
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819853

Digital Object Identifier
doi:10.1214/EJP.v15-839

Mathematical Reviews number (MathSciNet)
MR2745726

Zentralblatt MATH identifier
1231.60037

Subjects
Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60K37: Processes in random environments

Keywords
Markov chains Random walk Random environments Random conductances Percolation

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Boukhadra, Omar. Standard Spectral Dimension for the Polynomial Lower Tail Random Conductances Model. Electron. J. Probab. 15 (2010), paper no. 68, 2069--2086. doi:10.1214/EJP.v15-839. https://projecteuclid.org/euclid.ejp/1464819853


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