Lyapunov exponents of random walks in small random potential: the upper bound

Mountford, Thomas; Mourrat, Jean-Christophe

doi:10.1214/ejp.v20-3489

Cited by 3 publications

(1 citation statement)

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“…In particular, it is shown there that both the quenched and the annealed Lyapunov exponents scale like c √ h as h tends to zero. This has been extended to the case when the potentials are not integrable in [49,50]. In a sense, our Green kernel bound in Theorem 3.8 partially extends the results in [47] to random walks under random conductances with correlated potentials.…”

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confidence: 57%

First passage percolation with long-range correlations and applications to random Schrödinger operators

Andrés¹,

Prévost²

2021

Preprint

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We consider first passage percolation (FPP) with passage times generated by a general class of models with long-range correlations on Z d , d ≥ 2, including discrete Gaussian free fields, Ginzburg-Landau ∇φ interface models or random interlacements as prominent examples. We show that the associated time constant is positive, the FPP distance is comparable to the Euclidean distance, and we obtain a shape theorem. We also present two applications for random conductance models (RCM) with possibly unbounded and strongly correlated conductances. Namely, we obtain a Gaussian heat kernel upper bound for RCMs with a general class of speed measures, and an exponential decay estimate for the Green function of RCMs with random killing measures.

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confidence: 57%