Diffusivity in one-dimensional generalized Mott variable-range hopping models

DOI10.1214/08-AAP583zbMath1173.60032arXivmath/0701253MaRDI QIDQ835067

Pietro Caputo, Alessandra Faggionato

Publication date: 27 August 2009

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701253

zbMATH Keywords

point processinvariance principlediffusivityMott variable-range hoping modelrandom walking environment

Mathematics Subject Classification ID

Processes in random environments (60K37) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (13)

The velocity of 1d Mott variable-range hopping with external field ⋮ Random walks in a one-dimensional Lévy random environment ⋮ Invariance principle for Mott variable range hopping and other walks on point processes ⋮ Heat kernels, stochastic processes and functional inequalities. Abstracts from the workshop held October 30 -- November 5, 2022 ⋮ Large fluctuations and transport properties of the Lévy-Lorentz gas ⋮ Stochastic homogenization of random walks on point processes ⋮ Anomalous scaling regime for one-dimensional Mott variable-range hopping ⋮ Dissipative dynamics in semiconductors at low temperature ⋮ Extremal regime for one-dimensional Mott variable-range hopping ⋮ Limit theorems for Lévy flights on a 1D Lévy random medium ⋮ Mott law as upper bound for a random walk in a random environment ⋮ Recurrence or transience of random walks on random graphs generated by point processes in \(\mathbb{R}^d\) ⋮ Einstein relation and linear response in one-dimensional Mott variable-range hopping

Cites Work

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• An invariance principle for reversible Markov processes. Applications to random motions in random environments
• Quenched invariance principle for simple random walk on percolation clusters
• Mott law as upper bound for a random walk in a random environment
• Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions
• An introduction to the theory of point processes
• Mott law as lower bound for a random walk in a random environment
• Isoperimetric inequalities and mixing time for a random walk on a random point process
• Limit theorems for random walks, birth and death processes, and diffusion processes
• Quenched invariance principles for random walks on percolation clusters

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