Results and conjectures on a toy model of depinning

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.

Sumitted to the Moscow Mathematical Journal for the volume dedicated to the memory of Roland Dobrushin

References in corpus (5)

• Fractional moment bounds and disorder relevance for pinning models
• Smoothing effect of quenched disorder on polymer depinning transitions
• Distribution of pseudo-critical temperatures and lack of self-averaging in disordered Poland-Scheraga models with different loop exponents
• Critical points of quadratic renormalizations of random variables and phase transitions of disordered polymer models on diamond lattices
• Strong Disorder Renewal Approach to DNA denaturation and wetting : typical and large deviation properties of the free energy

Cited by in corpus (2)

• A numerical investigation into the scaling behavior of the longest increasing subsequences of the symmetric ultra-fat tailed random walk
• Enumeration of fully parked trees