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2018 On the maximum of conditioned random walks and tightness for pinning models
Francesco Caravenna
Electron. Commun. Probab. 23(none): 1-13 (2018). DOI: 10.1214/18-ECP172

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.

Citation

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Francesco Caravenna. "On the maximum of conditioned random walks and tightness for pinning models." Electron. Commun. Probab. 23 1 - 13, 2018. https://doi.org/10.1214/18-ECP172

Information

Received: 1 June 2018; Accepted: 28 September 2018; Published: 2018
First available in Project Euclid: 12 October 2018

zbMATH: 1400.82099
MathSciNet: MR3866042
Digital Object Identifier: 10.1214/18-ECP172

Subjects:
Primary: 60B10, 60K35, 82B41

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