Short-Time Asymptotics of the Heat Kernel and Extreme Statistics of the NET

David Holcman, Zeev Schuss

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

The first of N i.i.d. Brownian trajectories that arrive at a small target sets a time scale which is much shorter than that of the arrival of a typical trajectory. The shortest arrival time is computed here analytically in an asymptotic approximation for large N. The asymptotic expression is computed here based on the short-time asymptotics of the pdf of the first time to a small target in 1, 2 and 3 dimensions. These are referred to in the statistical physics literature as extreme statistics.

Original languageEnglish
Title of host publicationApplied Mathematical Sciences (Switzerland)
PublisherSpringer
Pages311-340
Number of pages30
DOIs
StatePublished - 2018

Publication series

NameApplied Mathematical Sciences (Switzerland)
Volume199
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X

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