# Longest common substring for random subshifts of finite type

## TL;DR

This paper investigates the behavior of the longest common substring in random subshifts of finite type and random sequences, linking it to Rènyi entropy under exponential mixing conditions, with a focus on quenched results.

## Contribution

It establishes a connection between the longest common substring behavior and Rènyi entropy in random subshifts, providing quenched results under mixing assumptions.

## Key findings

- Behavior linked to Rènyi entropy
- Results hold under exponential mixing
- Focus on quenched analysis

## Abstract

In this paper, we study the behaviour of the longest common substring for random subshifts of finite type (for dynamicists) or of the longest common substring for random sequences in random environments (for probabilists). We prove that, under some exponential mixing assumptions, this behaviour is linked to the R\'enyi entropy of the stationary measure. We emphasize that what we establish is a quenched result.