Upper tail asymptotics for the intersection local times of random walks in high dimensions

Peter Mörters[1]

  • [1] University of Bath

Actes des rencontres du CIRM (2010)

  • Volume: 2, Issue: 1, page 27-29
  • ISSN: 2105-0597

Abstract

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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.

How to cite

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Mörters, Peter. "Upper tail asymptotics for the intersection local times of random walks in high dimensions." Actes des rencontres du CIRM 2.1 (2010): 27-29. <http://eudml.org/doc/115846>.

@article{Mörters2010,
abstract = {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.},
affiliation = {University of Bath},
author = {Mörters, Peter},
journal = {Actes des rencontres du CIRM},
language = {eng},
month = {12},
number = {1},
pages = {27-29},
publisher = {CIRM},
title = {Upper tail asymptotics for the intersection local times of random walks in high dimensions},
url = {http://eudml.org/doc/115846},
volume = {2},
year = {2010},
}

TY - JOUR
AU - Mörters, Peter
TI - Upper tail asymptotics for the intersection local times of random walks in high dimensions
JO - Actes des rencontres du CIRM
DA - 2010/12//
PB - CIRM
VL - 2
IS - 1
SP - 27
EP - 29
AB - 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.
LA - eng
UR - http://eudml.org/doc/115846
ER -

References

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  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. Zbl1170.60019MR2472140
  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. Zbl0044.14001MR47272
  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. Zbl0814.60063MR1311718
  4. W. König and P. Mörters. Brownian intersection local times: Upper tail asymptotics and thick points. Annals of Probability, 30 (2002) 1605-1656. Zbl1032.60073MR1944002

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