Annals of Probability

Large deviations for intersection local times in critical dimension

Fabienne Castell

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Abstract

Let (Xt, t≥0) be a continuous time simple random walk on ℤd (d≥3), and let lT(x) be the time spent by (Xt, t≥0) on the site x up to time T. We prove a large deviations principle for the q-fold self-intersection local time IT=∑x∈ℤdlT(x)q in the critical case q=d/(d−2). When q is integer, we obtain similar results for the intersection local times of q independent simple random walks.

Article information

Source
Ann. Probab., Volume 38, Number 2 (2010), 927-953.

Dates
First available in Project Euclid: 9 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.aop/1268143536

Digital Object Identifier
doi:10.1214/09-AOP499

Mathematical Reviews number (MathSciNet)
MR2642895

Zentralblatt MATH identifier
1195.60041

Subjects
Primary: 60F10: Large deviations 60J15 60J55: Local time and additive functionals

Keywords
Large deviations intersection local times

Citation

Castell, Fabienne. Large deviations for intersection local times in critical dimension. Ann. Probab. 38 (2010), no. 2, 927--953. doi:10.1214/09-AOP499. https://projecteuclid.org/euclid.aop/1268143536


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