Aging and sub-aging for one-dimensional random walks amongst random conductances

D. A. Croydon; D. Kious; C. Scali

doi:10.1016/j.spa.2025.104562

Aging and sub-aging for one-dimensional random walks amongst random conductances

D. A. Croydon
, D. Kious
, C. Scali

Kyoto University
Technical University of Munich

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

1 Citation (SciVal)

Abstract

We consider random walks amongst random conductances in the cases where the conductances can be arbitrarily small, with a heavy-tailed distribution at 0, and where the conductances may or may not have a heavy-tailed distribution at infinity. We study the long time behaviour of these processes and prove aging statements. When the heavy tail is only at 0, we prove that aging can be observed for the maximum of the process, i.e. the same maximal value is attained repeatedly over long time-scales. When there are also heavy tails at infinity, we prove a classical aging result for the position of the walker, as well as a sub-aging result that occurs on a shorter time-scale.

Original language	English
Article number	104562
Number of pages	38
Journal	Stochastic Processes and their Applications
Volume	182
Early online date	9 Jan 2025
DOIs	https://doi.org/10.1016/j.spa.2025.104562
Publication status	Published - 30 Apr 2025

Funding

DK was partially supported by the EPSRC grant EP/V00929X/1. DC was supported by JSPS Grant -in-Aid for Scientific Research (C) 19K03540 and the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University. CS was supported by a scholarship from the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa) , under the project EP/S022945/1.

Funders	Funder number
Engineering and Physical Sciences Research Council	EP/V00929X/1
EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)	EP/S022945/1

Keywords

Aging
Blocking
Disordered media
Random conductance model
Random walk in random environment
Sub-aging
Trapping

ASJC Scopus subject areas

Statistics and Probability
Modelling and Simulation
Applied Mathematics

Access to Document

10.1016/j.spa.2025.104562Licence: CC BY

Cite this

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title = "Aging and sub-aging for one-dimensional random walks amongst random conductances",

abstract = "We consider random walks amongst random conductances in the cases where the conductances can be arbitrarily small, with a heavy-tailed distribution at 0, and where the conductances may or may not have a heavy-tailed distribution at infinity. We study the long time behaviour of these processes and prove aging statements. When the heavy tail is only at 0, we prove that aging can be observed for the maximum of the process, i.e. the same maximal value is attained repeatedly over long time-scales. When there are also heavy tails at infinity, we prove a classical aging result for the position of the walker, as well as a sub-aging result that occurs on a shorter time-scale.",

keywords = "Aging, Blocking, Disordered media, Random conductance model, Random walk in random environment, Sub-aging, Trapping",

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AU - Croydon, D. A.

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N2 - We consider random walks amongst random conductances in the cases where the conductances can be arbitrarily small, with a heavy-tailed distribution at 0, and where the conductances may or may not have a heavy-tailed distribution at infinity. We study the long time behaviour of these processes and prove aging statements. When the heavy tail is only at 0, we prove that aging can be observed for the maximum of the process, i.e. the same maximal value is attained repeatedly over long time-scales. When there are also heavy tails at infinity, we prove a classical aging result for the position of the walker, as well as a sub-aging result that occurs on a shorter time-scale.

AB - We consider random walks amongst random conductances in the cases where the conductances can be arbitrarily small, with a heavy-tailed distribution at 0, and where the conductances may or may not have a heavy-tailed distribution at infinity. We study the long time behaviour of these processes and prove aging statements. When the heavy tail is only at 0, we prove that aging can be observed for the maximum of the process, i.e. the same maximal value is attained repeatedly over long time-scales. When there are also heavy tails at infinity, we prove a classical aging result for the position of the walker, as well as a sub-aging result that occurs on a shorter time-scale.

KW - Aging

KW - Blocking

KW - Disordered media

KW - Random conductance model

KW - Random walk in random environment

KW - Sub-aging

KW - Trapping

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DO - 10.1016/j.spa.2025.104562

M3 - Article

AN - SCOPUS:85214950017

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VL - 182

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

M1 - 104562

ER -

Aging and sub-aging for one-dimensional random walks amongst random conductances

Abstract

Funding

Keywords

ASJC Scopus subject areas

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Random walks in dynamic random environment

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Aging and sub-aging for one-dimensional random walks amongst random conductances

Abstract

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

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Random walks in dynamic random environment

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