Large deviations for intersection local times in critical dimension

  title={Large deviations for intersection local times in critical dimension},
  author={Fabienne Castell},
Let (X t , t ≥ 0) be a continuous time simple random walk on Z d , and let l T (x) be the time spent by (X t , t ≥ 0) on the site x up to time T. We prove a large deviations principle for the q-fold self-intersection local time I T = x∈Z d l T (x) q in the critical dimension d = 2q q−1. When q is integer, we obtain similar results for the intersection local times of q independent simple random walks. 

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