2023/08/04 by David A. Croydon, Croydon, David A., Daniel Kious +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #60G50 #60G52 #60J27 #60K37 (primary) #82B41 #82D30 #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · doi:10.48550/arxiv.2308.02230
openalex publication_date 2023/08/04 · openalex created_date 2023/08/08 · openalex updated_date 2026/07/28
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.