Quasi-stationarity of the Dyson Brownian motion with collisions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918230593896448 |
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| author | Guillin, Arnaud Nectoux, Boris Wu, Liming |
| author_facet | Guillin, Arnaud Nectoux, Boris Wu, Liming |
| contents | In this work, we investigate the ergodic behavior of a system of particules, subject to collisions, before it exits a fixed subdomain of its state space. This system is composed of several one-dimensional ordered Brownian particules in interaction with electrostatic repulsions, which is usually referred as the (generalized) Dyson Brownian motion. The starting points of our analysis are the work [E. C{é}pa and D. L{é}pingle, 1997 Probab. Theory Relat. Fields] which provides existence and uniqueness of such a system subject to collisions via the theory of multivalued SDEs and a Krein-Rutman type theorem derived in [A. Guillin, B. Nectoux, L. Wu, 2020 J. Eur. Math. Soc.]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08467 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasi-stationarity of the Dyson Brownian motion with collisions Guillin, Arnaud Nectoux, Boris Wu, Liming Probability Mathematical Physics Data Analysis, Statistics and Probability In this work, we investigate the ergodic behavior of a system of particules, subject to collisions, before it exits a fixed subdomain of its state space. This system is composed of several one-dimensional ordered Brownian particules in interaction with electrostatic repulsions, which is usually referred as the (generalized) Dyson Brownian motion. The starting points of our analysis are the work [E. C{é}pa and D. L{é}pingle, 1997 Probab. Theory Relat. Fields] which provides existence and uniqueness of such a system subject to collisions via the theory of multivalued SDEs and a Krein-Rutman type theorem derived in [A. Guillin, B. Nectoux, L. Wu, 2020 J. Eur. Math. Soc.]. |
| title | Quasi-stationarity of the Dyson Brownian motion with collisions |
| topic | Probability Mathematical Physics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2504.08467 |