# A max-type recursive model: some properties and open questions

## TL;DR

This paper investigates a max-type recursive model related to depinning transitions, analyzing its critical behavior including extinction probability and moments, and presents several conjectures on its properties.

## Contribution

It introduces a detailed analysis of the critical regime of a max-type recursive model, highlighting new properties and open questions.

## Key findings

- Analysis of extinction probability in the critical regime
- Results on the first moment and moment generating function
- Identification of open conjectures for future research

## Abstract

We consider a simple max-type recursive model which was introduced in the study of depinning transition in presence of strong disorder, by Derrida and Retaux. Our interest is focused on the critical regime, for which we study the extinction probability, the first moment and the moment generating function. Several stronger assertions are stated as conjectures.