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

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

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Article number104562
JournalStochastic Processes and their Applications
Volume182
Early online date9 Jan 2025
DOIs
Publication statusE-pub ahead of print - 9 Jan 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.

FundersFunder number
Engineering and Physical Sciences Research CouncilEP/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

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