Translator Disclaimer
2012 Large deviations for self-intersection local times in subcritical dimensions
Clément Laurent
Author Affiliations +
Electron. J. Probab. 17: 1-20 (2012). DOI: 10.1214/EJP.v17-1874

Abstract

Let $(X_t,t\geq 0)$ be a simple symmetric random walk on $\mathbb{Z}^d$ and for any $x\in\mathbb{Z}^d$, let $ l_t(x)$ be its local time at site $x$. For any $p>1$, we denote by$ I_t= \sum\limits_{x\in\mathbb{Z}^d} l_t(x)^p $ the p-fold self-intersection local times (SILT). Becker and König recently proved a large deviations principle for $I_t$ for all $p>1$ such that $p(d-2/p)<2$. We extend these results to a broader scale of deviations and to the whole subcritical domain $p(d-2)<d$. Moreover, we unify the proofs of the large deviations principle using a method introduced by Castell for the critical case $p(d-2)=d$.

Citation

Download Citation

Clément Laurent. "Large deviations for self-intersection local times in subcritical dimensions." Electron. J. Probab. 17 1 - 20, 2012. https://doi.org/10.1214/EJP.v17-1874

Information

Accepted: 14 March 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1245.60036
MathSciNet: MR2900462
Digital Object Identifier: 10.1214/EJP.v17-1874

Subjects:
Primary: 60F10
Secondary: 60G50, 60J27, 60J55

JOURNAL ARTICLE
20 PAGES


SHARE
Vol.17 • 2012
Back to Top