Invariance principle for Mott variable range hopping and other walks on point processes

P. Caputo; A. Faggionato; T. Prescott

Annales de l'I.H.P. Probabilités et statistiques (2013)

  • Volume: 49, Issue: 3, page 654-697
  • ISSN: 0246-0203

Abstract

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We consider a random walk on a homogeneous Poisson point process with energy marks. The jump rates decay exponentially in the α -power of the jump length and depend on the energy marks via a Boltzmann-like factor. The case α = 1 corresponds to the phonon-induced Mott variable range hopping in disordered solids in the regime of strong Anderson localization. We prove that for almost every realization of the marked process, the diffusively rescaled random walk, with an arbitrary start point, converges to a Brownian motion whose diffusion matrix is positive definite and independent of the environment. Finally, we extend the above result to other point processes including diluted lattices.

How to cite

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Caputo, P., Faggionato, A., and Prescott, T.. "Invariance principle for Mott variable range hopping and other walks on point processes." Annales de l'I.H.P. Probabilités et statistiques 49.3 (2013): 654-697. <http://eudml.org/doc/272074>.

@article{Caputo2013,
abstract = {We consider a random walk on a homogeneous Poisson point process with energy marks. The jump rates decay exponentially in the $\alpha $-power of the jump length and depend on the energy marks via a Boltzmann-like factor. The case $\alpha =1$ corresponds to the phonon-induced Mott variable range hopping in disordered solids in the regime of strong Anderson localization. We prove that for almost every realization of the marked process, the diffusively rescaled random walk, with an arbitrary start point, converges to a Brownian motion whose diffusion matrix is positive definite and independent of the environment. Finally, we extend the above result to other point processes including diluted lattices.},
author = {Caputo, P., Faggionato, A., Prescott, T.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {random walk in random environment; Poisson point process; percolation; stochastic domination; invariance principle; corrector},
language = {eng},
number = {3},
pages = {654-697},
publisher = {Gauthier-Villars},
title = {Invariance principle for Mott variable range hopping and other walks on point processes},
url = {http://eudml.org/doc/272074},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Caputo, P.
AU - Faggionato, A.
AU - Prescott, T.
TI - Invariance principle for Mott variable range hopping and other walks on point processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2013
PB - Gauthier-Villars
VL - 49
IS - 3
SP - 654
EP - 697
AB - We consider a random walk on a homogeneous Poisson point process with energy marks. The jump rates decay exponentially in the $\alpha $-power of the jump length and depend on the energy marks via a Boltzmann-like factor. The case $\alpha =1$ corresponds to the phonon-induced Mott variable range hopping in disordered solids in the regime of strong Anderson localization. We prove that for almost every realization of the marked process, the diffusively rescaled random walk, with an arbitrary start point, converges to a Brownian motion whose diffusion matrix is positive definite and independent of the environment. Finally, we extend the above result to other point processes including diluted lattices.
LA - eng
KW - random walk in random environment; Poisson point process; percolation; stochastic domination; invariance principle; corrector
UR - http://eudml.org/doc/272074
ER -

References

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