Self-intersection local times of random walks : exponential moments in subcritical dimensions
Date
2010
Authors
Volume
1532
Issue
Journal
Series Titel
WIAS Preprints
Book Title
Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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Abstract
Fix p>1, not necessarily integer, with p(d-2)0 that are bounded from above, possibly tending to zero. The speed is identified in terms of mixed powers of t and theta_t, and the precise rate is characterized in terms of a variational formula, which is in close connection to the it Gagliardo-Nirenberg inequality. As a corollary, we obtain a large-deviation principle for ell_t _p/(t r_t) for deviation functions r_t satisfying t r_tggE[ ell_t _p]. Informally, it turns out that the random walk homogeneously squeezes in a t-dependent box with diameter of order ll t^1/d to produce the required amount of self-intersections. Our main tool is an upper bound for the joint density of the local times of the walk.
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Citation
Becker, M., & König, W. (2010). Self-intersection local times of random walks : exponential moments in subcritical dimensions. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.