Upper tail large deviations for Brownian motions with one-sided collisions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916656741089280 |
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| author | Weiss, Thomas |
| author_facet | Weiss, Thomas |
| contents | The system of interacting Brownian motions, where a particle is reflected asymmetrically from its left neighbor, belongs to the KPZ universality class, with multi-point asymptotics having been derived in previous works. In this paper we show upper tail large deviation principles for all three fundamental initial conditions, including explicit calculation of the rate function. For the periodic case the Lambert-W function, which is already present in the Fredholm determinant formula, also appears in the rate function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15018 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Upper tail large deviations for Brownian motions with one-sided collisions Weiss, Thomas Probability Mathematical Physics 60K35, 60J65, 60F10 The system of interacting Brownian motions, where a particle is reflected asymmetrically from its left neighbor, belongs to the KPZ universality class, with multi-point asymptotics having been derived in previous works. In this paper we show upper tail large deviation principles for all three fundamental initial conditions, including explicit calculation of the rate function. For the periodic case the Lambert-W function, which is already present in the Fredholm determinant formula, also appears in the rate function. |
| title | Upper tail large deviations for Brownian motions with one-sided collisions |
| topic | Probability Mathematical Physics 60K35, 60J65, 60F10 |
| url | https://arxiv.org/abs/2503.15018 |