Non-Gaussian fluctuations of randomly trapped random walks

2018/12/06 by Bowditch, Adam
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1812.02369

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 Lévy 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.

Related

• Stable limit laws for randomly biased walks on supercritical trees
• Central limit theorems for biased randomly trapped random walks on Z
• The slow regime of randomly biased walks on trees
• Scaling limit of the subdiffusive random walk on a Galton-Watson tree in random environment
• Biased random walk on critical Galton-Watson trees conditioned to\n survive