Ages of Records in Random Walks

Reka Szabo; Balint Veto

doi:10.1007/s10955-016-1671-0

Ages of Records in Random Walks

Reka Szabo, Balint Veto^*

^*Corresponding author for this work

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Abstract

We consider random walks with continuous and symmetric step distributions. We prove universal asymptotics for the average proportion of the age of the kth longest lasting record for and for the probability that the record of the kth longest age is broken at step n. Due to the relation to the Chinese restaurant process, the ranked sequence of proportions of ages converges to the Poisson-Dirichlet distribution.

Original language	English
Pages (from-to)	1086-1101
Number of pages	16
Journal	Journal of Statistical Physics
Volume	165
Issue number	6
DOIs	https://doi.org/10.1007/s10955-016-1671-0
Publication status	Published - Dec-2016

Keywords

Longest lasting records
Random walk
Asymptotic average proportion
Laplace transform
Renewal process
Poisson-Dirichlet distribution
STABLE SUBORDINATOR
PARTITIONS
EXCURSION

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title = "Ages of Records in Random Walks",

abstract = "We consider random walks with continuous and symmetric step distributions. We prove universal asymptotics for the average proportion of the age of the kth longest lasting record for and for the probability that the record of the kth longest age is broken at step n. Due to the relation to the Chinese restaurant process, the ranked sequence of proportions of ages converges to the Poisson-Dirichlet distribution.",

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AU - Szabo, Reka

AU - Veto, Balint

PY - 2016/12

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N2 - We consider random walks with continuous and symmetric step distributions. We prove universal asymptotics for the average proportion of the age of the kth longest lasting record for and for the probability that the record of the kth longest age is broken at step n. Due to the relation to the Chinese restaurant process, the ranked sequence of proportions of ages converges to the Poisson-Dirichlet distribution.

AB - We consider random walks with continuous and symmetric step distributions. We prove universal asymptotics for the average proportion of the age of the kth longest lasting record for and for the probability that the record of the kth longest age is broken at step n. Due to the relation to the Chinese restaurant process, the ranked sequence of proportions of ages converges to the Poisson-Dirichlet distribution.

KW - Longest lasting records

KW - Random walk

KW - Asymptotic average proportion

KW - Laplace transform

KW - Renewal process

KW - Poisson-Dirichlet distribution

KW - STABLE SUBORDINATOR

KW - PARTITIONS

KW - EXCURSION

U2 - 10.1007/s10955-016-1671-0

DO - 10.1007/s10955-016-1671-0

M3 - Article

SN - 0022-4715

VL - 165

SP - 1086

EP - 1101

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 6

ER -

Ages of Records in Random Walks

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Keywords

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