Results and conjectures on a toy model of depinning

2020/05/20 by Bernard Derrida, Derrida, Bernard, Zhan Shi +1
Mathematics · #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2005.10208

openalex publication_date 2020/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We review recent results and conjectures for a simplified version of the depinning problem in presence of disorder which was introduced by Derrida and Retaux in 2014. For this toy model, the depinning transition has been predicted to be of the Berezinskii--Kosterlitz--Thouless type. Here we discuss under which integrability conditions this prediction can be proved and how it is modified otherwise.

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