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Upper tail asymptotics for the intersection local times of random walks in high dimensions
Peter Mörters1
1 University of Bath
Actes des rencontres du CIRM, Volume 2 (2010) no. 1, pp. 27-29.

In high dimensions two independent simple random walks have only a finite number of intersections. I describe the main result obtained in a joint paper with Xia Chen in which we determine the exact upper tail behaviour of the intersection local time.

Published online:
DOI: 10.5802/acirm.20
Peter Mörters 1

1 University of Bath 
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Peter Mörters. Upper tail asymptotics for the intersection local times of random walks in high dimensions. Actes des rencontres du CIRM, Volume 2 (2010) no. 1, pp. 27-29. doi : 10.5802/acirm.20. https://acirm.centre-mersenne.org/articles/10.5802/acirm.20/

[1] X. Chen and P. Mörters. Upper tails for intersection local times of random walks in supercritial dimensions. Journal of the London Mathematical Society, 79 (2009) 186-210. | DOI | MR | Zbl

[2] A. Dvoretzky and P. Erdős. Some problems on random walk in space. In: Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950. University of California Press, Berkeley and Los Angeles, pp. 353–367, 1951.

[3] K.M. Khanin, A.E. Mazel, S.B. Shlosman and Ya.G. Sinai. Loop condensation effects in the behavior of random walks. In: Markov processes and applications, Birkhäuser, pp. 167–184, 1994. | DOI | Zbl

[4] W. König and P. Mörters. Brownian intersection local times: Upper tail asymptotics and thick points. Annals of Probability, 30 (2002) 1605-1656. | DOI | MR | Zbl

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