An exactly solvable continuous-time Derrida--Retaux model
Abstract
To study the depinning transition in the limit of strong disorder, Derrida and Retaux (2014) introduced a discrete-time max-type recursive model. It is believed that for a large class of recursive models, including Derrida and Retaux' model, there is a highly non-trivial phase transition. In this article, we present a continuous-time version of Derrida and Retaux model, built on a Yule tree, which yields an exactly solvable model belonging to this universality class. The integrability of this model allows us to study in details the phase transition near criticality and can be used to confirm the infinite order phase transition predicted by physicists. We also study the scaling limit of this model at criticality, which we believe to be universal.
Cite
@article{arxiv.1811.08749,
title = {An exactly solvable continuous-time Derrida--Retaux model},
author = {Yueyun Hu and Bastien Mallein and Michel Pain},
journal= {arXiv preprint arXiv:1811.08749},
year = {2019}
}
Comments
47 pages, 9 figures, minor changes. To appear in Communications in Mathematical Physics