# Recurrence of the frog model on the 3,2-alternating tree

## TL;DR

This paper proves that the frog model on a 3,2-alternating tree, where nodes alternate between having two and three children, is recurrent, meaning infinitely many frogs will hit the root with probability one.

## Contribution

It extends the recurrence result of the frog model from regular binary trees to the more complex 3,2-alternating tree structure.

## Key findings

- Proves recurrence of the frog model on the 3,2-alternating tree.
- Builds on recent proofs for binary trees.
- Establishes that infinitely many frogs hit the root with probability one.

## Abstract

Consider a growing system of random walks on the 3,2-alternating tree, where generations of nodes alternate between having two and three children. Any time a particle lands on a node which has not been visited previously, a new particle is activated at that node, and begins its own random walk. The model described belongs to a class of problems that are collectively referred to as the frog model. Building on a recent proof of recurrence (meaning infinitely many frogs hit the root with probability one) on the regular binary tree, this paper establishes recurrence for the 3,2-alternating case.