On the maximum of conditioned random walks and tightness for pinning models

Electronic Communications in Probability

Francesco Caravenna¹ 

关键词: random walk;    bridge;    excursion;    conditioning to stay positive;    uniform integrability;    polymer model;    pinning model;    wetting model;    tightness;   

DOI  :  10.1214/18-ECP172

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

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.

【 授权许可】

CC BY