Derrida-Retaux type models and related scaling limit theorems

TL;DR

This paper characterizes the transition semigroup and generator of a continuous-time Derrida-Retaux type process, demonstrating its emergence as a scaling limit of discrete max-type recursive models, thus advancing understanding of these stochastic processes.

Contribution

It provides a new characterization of the continuous-time Derrida-Retaux process and links it to discrete models through scaling limits, extending prior work.

Findings

Characterization of the transition semigroup and generator of the process

Establishment of the process as a scaling limit of discrete models

Connection between continuous and discrete Derrida-Retaux models

Abstract

We give characterizations of the transition semigroup and generator of a continuous-time Derrida--Retaux type process that generalizes the one introduced by Hu, Mallein and Pain (Commun. Math. Phys., 2020). It is shown that the process arises naturally as the scaling limit of the discrete-time max-type recursive models introduced by Hu and Shi (J. Stat. Phys., 2018).