Central limit theorems for biased randomly trapped random walks on Z
Abstract
We prove CLTs for biased randomly trapped random walks in one dimension. In particular, we will establish an annealed invariance principal by considering a sequence of regeneration times under the assumption that the trapping times have finite second moment. In a quenched environment, an environment dependent centring is determined which is necessary to achieve a central limit theorem. As our main motivation, we apply these results to biased walks on subcritical GaltonWatson trees conditioned to survive and prove a tight bound on the bias required to obtain such limiting behaviour.
 Publication:

arXiv eprints
 Pub Date:
 November 2016
 arXiv:
 arXiv:1611.06879
 Bibcode:
 2016arXiv161106879B
 Keywords:

 Mathematics  Probability;
 60K37;
 60F05;
 60F17;
 60J80
 EPrint:
 34 pages