Asymptotic analysis for the Generalized Relativistic Langevin Equation
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918391230496768 |
|---|---|
| author | Baker, Ethan Duong, Manh Hong Nguyen, Hung Dang |
| author_facet | Baker, Ethan Duong, Manh Hong Nguyen, Hung Dang |
| contents | In this paper, we study a non-Markovian generalized relativistic Langevin equation (GRLE). We show that when the memory kernel is a sum of exponentials, the GRLE is equivalent to a Markovian system with added variables. We establish the well-posedness and polynomial ergodicity, obtaining an algebraic rate of convergence to the unique Gibbs distribution. From the Markovian GRLE, we recover the relativistic underdamped Langevin dynamics in a small-noise limit, as well as the classical (non-relativistic) generalized Langevin dynamics in the Newtonian limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15088 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic analysis for the Generalized Relativistic Langevin Equation Baker, Ethan Duong, Manh Hong Nguyen, Hung Dang Probability In this paper, we study a non-Markovian generalized relativistic Langevin equation (GRLE). We show that when the memory kernel is a sum of exponentials, the GRLE is equivalent to a Markovian system with added variables. We establish the well-posedness and polynomial ergodicity, obtaining an algebraic rate of convergence to the unique Gibbs distribution. From the Markovian GRLE, we recover the relativistic underdamped Langevin dynamics in a small-noise limit, as well as the classical (non-relativistic) generalized Langevin dynamics in the Newtonian limit. |
| title | Asymptotic analysis for the Generalized Relativistic Langevin Equation |
| topic | Probability |
| url | https://arxiv.org/abs/2603.15088 |