# Backbone scaling limits for random walks on random critical trees

## TL;DR

This paper establishes the scaling limits of projected random walks on critical percolation clusters, showing they converge to spatially subordinated Brownian motions, thus advancing understanding of random walk behavior on complex random structures.

## Contribution

It introduces a novel approach by treating projected random walks as trapped random walks and derives their scaling limits as subordinated Brownian motions.

## Key findings

- Scaling limits exist for projected random walks on critical clusters.
- Projected walks converge to spatially subordinated Brownian motions.
- Provides a framework for analyzing random walks on complex random trees.

## Abstract

We prove the existence of scaling limits for the projection on the backbone of the random walks on the Incipient Infinite Cluster and the Invasion Percolation Cluster on a regular tree. We treat these projected random walks as randomly trapped random walks (as defined in [BC\v{C}R15]) and thus describe these scaling limits as spatially subordinated Brownian motions