Standard Spectral Dimension for the Polynomial Lower Tail Random\n Conductances model

2009/07/26 by Omar Boukhadra, Boukhadra, Omar
Mathematics · Physics and Astronomy · #60G50 #60J10 #60K37 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.0907.4525

openalex publication_date 2009/07/26 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We study models of continuous-time, symmetric, Z^d-valued random walks\nin random environments, driven by a field of i.i.d. random nearest-neighbor\nconductances \ω_xy\∈[0,1] with a power law with an exponent \γ\nnear 0. We are interested in estimating the quenched decay of the return\nprobability P_\ω^t(0,0), as t tends to +\∞. We show that for\n\γ> \(d)/(2), the standard bound turns out to be of the correct\nlogarithmic order. As an expected concequence, the same result holds for the\ndiscrete-time case.\n

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