The Tail of the Length of an Excursion in a Trap of Random Size

Nina Gantert; Achim Klenke

doi:10.1007/s10955-022-02957-9

The Tail of the Length of an Excursion in a Trap of Random Size

Nina Gantert
, Achim Klenke

Chair of Probability Theory

Johannes Gutenberg University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Consider a random walk with a drift to the right on { 0 , … , k} where k is random and geometrically distributed. We show that the tail P[T> t] of the length T of an excursion from 0 decreases up to constants like t^-^ϱ for some ϱ> 0 but is not regularly varying. We compute the oscillations of tϱP[T>t] as t→ ∞ explicitly.

Original language	English
Article number	27
Journal	Journal of Statistical Physics
Volume	188
Issue number	3
DOIs	https://doi.org/10.1007/s10955-022-02957-9
State	Published - Sep 2022

Keywords

Excursions of random walks
Tail of the population size in a branching process in random environment
Tails of hitting times
Trapping phenomena

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10.1007/s10955-022-02957-9

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abstract = "Consider a random walk with a drift to the right on \{ 0 , … , k\} where k is random and geometrically distributed. We show that the tail P[T> t] of the length T of an excursion from 0 decreases up to constants like t-ϱ for some ϱ> 0 but is not regularly varying. We compute the oscillations of tϱP[T>t] as t→ ∞ explicitly.",

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KW - Excursions of random walks

KW - Tail of the population size in a branching process in random environment

KW - Tails of hitting times

KW - Trapping phenomena

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The Tail of the Length of an Excursion in a Trap of Random Size

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Keywords

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