Aging and sub-aging for one-dimensional random walks amongst random conductances
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914680783503360 |
|---|---|
| author | Croydon, David A. Kious, Daniel Scali, Carlo |
| author_facet | Croydon, David A. Kious, Daniel Scali, Carlo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_02230 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Aging and sub-aging for one-dimensional random walks amongst random conductances Croydon, David A. Kious, Daniel Scali, Carlo Probability 60K37 (primary), 60G50, 60G52, 60J27, 82B41, 82D30 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. |
| title | Aging and sub-aging for one-dimensional random walks amongst random conductances |
| topic | Probability 60K37 (primary), 60G50, 60G52, 60J27, 82B41, 82D30 |
| url | https://arxiv.org/abs/2308.02230 |