Finite-time blowup of a Brownian particle in a repulsive potential
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909761898807296 |
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| author | Krapivsky, P. L. Meerson, Baruch |
| author_facet | Krapivsky, P. L. Meerson, Baruch |
| contents | We consider a Brownian particle performing an overdamped motion in a power-law repulsive potential. If the potential grows with the distance faster than quadratically, the particle escapes to infinity in a finite time. We determine the average blowup time and study the probability distribution of the blowup time. In particular, we show that the long-time tail of this probability distribution decays purely exponentially, while the short-time tail exhibits an essential singularity. These qualitative features turn out to be quite universal, as they occur for all rapidly growing power-law potentials in arbitrary spatial dimensions. The quartic potential is especially tractable, and we analyze it in more detail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11796 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite-time blowup of a Brownian particle in a repulsive potential Krapivsky, P. L. Meerson, Baruch Statistical Mechanics Mathematical Physics Probability We consider a Brownian particle performing an overdamped motion in a power-law repulsive potential. If the potential grows with the distance faster than quadratically, the particle escapes to infinity in a finite time. We determine the average blowup time and study the probability distribution of the blowup time. In particular, we show that the long-time tail of this probability distribution decays purely exponentially, while the short-time tail exhibits an essential singularity. These qualitative features turn out to be quite universal, as they occur for all rapidly growing power-law potentials in arbitrary spatial dimensions. The quartic potential is especially tractable, and we analyze it in more detail. |
| title | Finite-time blowup of a Brownian particle in a repulsive potential |
| topic | Statistical Mechanics Mathematical Physics Probability |
| url | https://arxiv.org/abs/2502.11796 |