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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.01703 |
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| _version_ | 1866916812010029056 |
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| author | Chen, Yu-Ting |
| author_facet | Chen, Yu-Ting |
| contents | This paper is the first in a series devoted to constructing stochastic motions for the two-dimensional $N$-body delta-Bose gas for all integers $N\geq 3$ and establishing the associated Feynman-Kac-type formulas; see [12,13,14] for the remaining of the series. The main results of this paper establish the foundation by studying the stochastic one-$δ$ motions, which relate to the two-dimensional many-body delta-Bose gas by turning off all but one delta function, and we prove the central distributional properties and the SDEs. The proofs extend the method in [11] for the stochastic relative motions and develop and use analytical formulas of the probability distributions of the stochastic one-$δ$ motions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01703 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic motions of the two-dimensional many-body delta-Bose gas, I: One-$δ$ motions Chen, Yu-Ting Probability This paper is the first in a series devoted to constructing stochastic motions for the two-dimensional $N$-body delta-Bose gas for all integers $N\geq 3$ and establishing the associated Feynman-Kac-type formulas; see [12,13,14] for the remaining of the series. The main results of this paper establish the foundation by studying the stochastic one-$δ$ motions, which relate to the two-dimensional many-body delta-Bose gas by turning off all but one delta function, and we prove the central distributional properties and the SDEs. The proofs extend the method in [11] for the stochastic relative motions and develop and use analytical formulas of the probability distributions of the stochastic one-$δ$ motions. |
| title | Stochastic motions of the two-dimensional many-body delta-Bose gas, I: One-$δ$ motions |
| topic | Probability |
| url | https://arxiv.org/abs/2505.01703 |