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

• Main Authors: Croydon, David A, Kious, Daniel, Scali, Carlo
• Format: Journal Article
• Language: English
• Published: 04-08-2023
• Subjects: Mathematics - Probability
• DOI: 10.48550/arxiv.2308.02230

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.