Upper tails of self-intersection local times of random walks: survey of proof techniques

Wolfgang König[1]

  • [1] Technical University Berlin, Str. des 17. Juni 136, 10623 Berlin, and Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany

Actes des rencontres du CIRM (2010)

  • Volume: 2, Issue: 1, page 15-24
  • ISSN: 2105-0597

Abstract

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The asymptotics of the probability that the self-intersection local time of a random walk on ℤ d exceeds its expectation by a large amount is a fascinating subject because of its relation to some models from Statistical Mechanics, to large-deviation theory and variational analysis and because of the variety of the effects that can be observed. However, the proof of the upper bound is notoriously difficult and requires various sophisticated techniques. We survey some heuristics and some recently elaborated techniques and results. This is an extended summary of a talk held on the CIRM-conference on Excess self-intersection local times, and related topics in Luminy, 6-10 Dec., 2010.

How to cite

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König, Wolfgang. "Upper tails of self-intersection local times of random walks: survey of proof techniques." Actes des rencontres du CIRM 2.1 (2010): 15-24. <http://eudml.org/doc/115843>.

@article{König2010,
abstract = {The asymptotics of the probability that the self-intersection local time of a random walk on $\mathbb\{Z\}^d$ exceeds its expectation by a large amount is a fascinating subject because of its relation to some models from Statistical Mechanics, to large-deviation theory and variational analysis and because of the variety of the effects that can be observed. However, the proof of the upper bound is notoriously difficult and requires various sophisticated techniques. We survey some heuristics and some recently elaborated techniques and results. This is an extended summary of a talk held on the CIRM-conference on Excess self-intersection local times, and related topics in Luminy, 6-10 Dec., 2010.},
affiliation = {Technical University Berlin, Str. des 17. Juni 136, 10623 Berlin, and Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany},
author = {König, Wolfgang},
journal = {Actes des rencontres du CIRM},
keywords = {Self-intersection local time; upper tail; Donsker-Varadhan large deviations; variational formula},
language = {eng},
month = {12},
number = {1},
pages = {15-24},
publisher = {CIRM},
title = {Upper tails of self-intersection local times of random walks: survey of proof techniques},
url = {http://eudml.org/doc/115843},
volume = {2},
year = {2010},
}

TY - JOUR
AU - König, Wolfgang
TI - Upper tails of self-intersection local times of random walks: survey of proof techniques
JO - Actes des rencontres du CIRM
DA - 2010/12//
PB - CIRM
VL - 2
IS - 1
SP - 15
EP - 24
AB - The asymptotics of the probability that the self-intersection local time of a random walk on $\mathbb{Z}^d$ exceeds its expectation by a large amount is a fascinating subject because of its relation to some models from Statistical Mechanics, to large-deviation theory and variational analysis and because of the variety of the effects that can be observed. However, the proof of the upper bound is notoriously difficult and requires various sophisticated techniques. We survey some heuristics and some recently elaborated techniques and results. This is an extended summary of a talk held on the CIRM-conference on Excess self-intersection local times, and related topics in Luminy, 6-10 Dec., 2010.
LA - eng
KW - Self-intersection local time; upper tail; Donsker-Varadhan large deviations; variational formula
UR - http://eudml.org/doc/115843
ER -

References

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