Large deviations estimates for self-intersection local times for simple random walk in \({\mathbb{Z}}^3\). (English) Zbl 1135.60340

Summary: We obtain large deviations estimates for the self-intersection local times for a simple 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 an application of our estimates to moderate deviations for random walk in random sceneries.


60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C22 Interacting particle systems in time-dependent statistical mechanics
60J25 Continuous-time Markov processes on general state spaces
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