# Talk

Modul:   MAT971  Stochastische Prozesse

## The Derrida-Retaux conjecture on recursive models

Prof. Dr. Yueyun Hu talk

Speaker invited by: Prof. Dr. Jean Bertoin

Date: 30.10.19  Time: 17.15 - 18.15  Room: ETH HG G 43

This talk is based on a joint work with Xinxing Chen, Victor Dagard, Bernard Derrida, Mikhail Lifshits, and Zhan Shi. We study a max-type recursive model which was introduced by Derrida and Retaux (2014) as a simplified hierarchical renormalization model to understand the depinning transition of a line in presence of strong disorder. It is expected to have many universality properties at or near criticality, though few of these predicted properties have been rigorously proved so far. In the nearly supercritical regime we prove that under a suitable integrability assumption on the initial distribution, the free energy vanishes at the transition with an essential singularity with exponent 1/2. This gives a weaker answer to a conjecture of Derrida and Retaux (2014). Other behaviours are obtained when the integrability condition is not satisfied.