Large deviations estimates for self-intersection local times for simple random walk in \Z³

2006/02/04 by Asselah, Amine
#60J25 #60K35 #82C22 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.math/0602074

Abstract

We obtain large deviations estimates for the self-intersection local times for a symmetric random walk in dimension 3. Also, we show that the main contribution to making the self-intersection large, in a time period of length n, comes from sites visited less than some power of log(n). This is opposite to the situation in dimensions larger or equal to 5. Finally, we present two applications of our estimates: (i) to moderate deviations estimates for the range of a random walk, and (ii) to moderate deviations for random walk in random sceneries.

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