# The free energy in the Derrida--Retaux recursive model

## TL;DR

This paper investigates the free energy behavior in a max-type recursive model from physics, focusing on the nearly supercritical regime to determine the range of the exponent.

## Contribution

It provides a detailed analysis of the free energy exponent in the Derrida-Retaux recursive model near the supercritical phase, extending understanding of its asymptotic properties.

## Key findings

- Identifies the range of the free energy exponent in the nearly supercritical regime.
- Provides mathematical characterization of the free energy behavior.
- Extends previous work on Derrida-Retaux models in statistical physics.

## Abstract

We are interested in a simple max-type recursive model studied by Derrida and Retaux (2014) in the context of a physics problem, and find a wide range for the exponent in the free energy in the nearly supercritical regime.