Marginal relevance for the γ-stable pinning model

2016/12/07 by Hubert Lacoin, Lacoin, Hubert
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1612.02389

openalex publication_date 2016/12/07 · openalex created_date 2022/09/21 · openalex updated_date 2026/07/28

Abstract

We investigate disorder relevance for the pinning of a renewal when the law of the random environment is in the domain of attraction of a stable law with parameter γ∈ (1,2). Assuming that the renewal jumps have power-law decay, we determine under which condition the critical point of the system modified by the introduction of a small quantity of disorder. In an earlier study of the problem, we have shown that the answer depends on the value of the tail exponent α associated to the distribution of renewal jumps: when α>1-γ^-1 a small amount of disorder shifts the critical point whereas it does not when α<1-γ^-1. The present paper is focused on the boundary case α=1-γ^-1. We show that a critical point shifts occurs in this case, and obtain an estimate for its intensity.

Citations

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