# Frog models on trees through renewal theory

## TL;DR

This paper analyzes frog models with geometric lifetime on regular trees using renewal theory, deriving improved bounds for critical parameters and advancing understanding of related percolation models.

## Contribution

It introduces a renewal theory approach to obtain tighter bounds for critical parameters in frog models and cone percolation on trees, enhancing previous results.

## Key findings

- Derived new bounds for frog model critical parameters
- Improved bounds for cone percolation critical parameters
- Applied renewal theory to analyze growing systems of random walks

## Abstract

This paper studies a class of growing systems of random walks on regular trees, known as \emph{frog models with geometric lifetime} in the literature. With the help of results from renewal theory, we derive new bounds for their critical parameters. Our approach also improve the bounds of the literature for the critical parameter of a percolation model on trees called \emph{cone percolation}