# Stability and instability of steady states for a branching random walk

## TL;DR

This paper investigates the behavior of a lattice branching random walk with local perturbations, establishing conditions for the existence of steady states and deriving moment estimates using Carleman-type inequalities.

## Contribution

It introduces new Carleman-type estimates for moments and proves the existence of steady states in perturbed lattice branching random walks.

## Key findings

- Existence of steady states under certain conditions
- Carleman-type estimates for moments of subpopulations
- Conditions for stability and instability of steady states

## Abstract

We consider the time evolution of a lattice branching random walk with local perturbations. Under certain conditions, we prove the Carleman type estimation for the moments of a particle subpopulation number and show the existence of a steady state.