# Non-Gaussian fluctuations of randomly trapped random walks

## TL;DR

This paper studies one-dimensional biased randomly trapped random walks with infinite variance trapping times, showing they converge to a stable Lévy process and confirming non-Gaussian fluctuation behavior on certain trees.

## Contribution

It provides new conditions for convergence to stable Lévy processes and applies these to biased walks on Galton-Watson trees, revealing non-Gaussian fluctuation regimes.

## Key findings

- Convergence to stable Lévy processes under infinite variance trapping times.
- Identification of non-Gaussian fluctuation regimes for biased walks.
- Application to Galton-Watson trees confirms fluctuation order.

## Abstract

In this paper we consider the one-dimensional, biased, randomly trapped random walk when the trapping times have infinite variance. We prove sufficient conditions for the suitably scaled walk to converge to a transformation of a stable L\'{e}vy process. As our main motivation, we apply subsequential versions of our results to biased walks on subcritical Galton-Watson trees conditioned to survive. This confirms the correct order of the fluctuations of the walk around its speed for values of the bias that yield a non-Gaussian regime.