Aging and sub-aging for one-dimensional random walks amongst random conductances
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. This models showcase two trapping phenomena: ``blocking'' is caused by atypically small conductances, and ''trapping'' by atypically large ones. When the heavy tail is only at 0, I will explain how one can quantify blocking and prove a related aging statement, i.e. show that the same maximal value can be attained repeatedly over long time-scales. When there are also heavy tails at infinity, I will present a classical aging result for the position of the walker, as well as a sub-aging result that occurs on a shorter time-scale. This is joint work with David Croydon and Daniel Kious.
Area: CS27 - Particle systems with spatial and self-interactions (Alice Callegaro)
Keywords: Random walk, aging, random media, blocking, trapping
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