Large deviations estimates for self-intersection local times for simple random walk in ${\mathbb{Z}}^3$

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.

23 pages

References in corpus (3)

• Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm
• Large deviations for renormalized self-intersection local times of stable processes
• A note on random walk in random scenery

Cited by in corpus (1)

• Moderate deviations for random walk in random scenery