On the maximum of conditioned random walks and tightness for pinning models
Probability
2018-10-18 v3
Abstract
We consider real random walks with finite variance. We prove an optimal integrability result for the diffusively rescaled maximum, when the walk or its bridge is conditioned to stay positive, or to avoid zero. As an application, we prove tightness under diffusive rescaling for general pinning and wetting models based on random walks.
Keywords
Cite
@article{arxiv.1805.10272,
title = {On the maximum of conditioned random walks and tightness for pinning models},
author = {Francesco Caravenna},
journal= {arXiv preprint arXiv:1805.10272},
year = {2018}
}
Comments
13 pages. Changed title, improved result (Theorem 3.2), fixed typos. Final version published in ECP