Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.14487 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915864622661632 |
|---|---|
| author | Pagnini, M. Dahlenburg G. |
| author_facet | Pagnini, M. Dahlenburg G. |
| contents | The first-return time is the time that it takes a random walker to go back to the initial position for the first time. We study the first-return time when random walkers perform fractional kinetics, specifically fractional diffusion, that is modelled within the framework of the continuous-time random walk on homogeneous space in the uncoupled formulation with Mittag-Leffler distributed waiting-times. We consider both Markovian and non-Markovian settings, as well as any kind of symmetric jump-size distributions, namely with finite or infinite variance. We show that the first-return time density is indeed independent of the jump-size distribution when it is symmetric, and therefore it is affected only by the waiting-time distribution that embodies the memory of the process. We perform our analysis in two cases: first jump then wait and first wait then jump, and we provide several exact results, including the relation between results in the Markovian and non-Markovian settings and the difference between the two cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14487 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | First-return time in fractional kinetics Pagnini, M. Dahlenburg G. Statistical Mechanics Mathematical Physics The first-return time is the time that it takes a random walker to go back to the initial position for the first time. We study the first-return time when random walkers perform fractional kinetics, specifically fractional diffusion, that is modelled within the framework of the continuous-time random walk on homogeneous space in the uncoupled formulation with Mittag-Leffler distributed waiting-times. We consider both Markovian and non-Markovian settings, as well as any kind of symmetric jump-size distributions, namely with finite or infinite variance. We show that the first-return time density is indeed independent of the jump-size distribution when it is symmetric, and therefore it is affected only by the waiting-time distribution that embodies the memory of the process. We perform our analysis in two cases: first jump then wait and first wait then jump, and we provide several exact results, including the relation between results in the Markovian and non-Markovian settings and the difference between the two cases. |
| title | First-return time in fractional kinetics |
| topic | Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2603.14487 |