Stochastic motions of the two-dimensional many-body delta-Bose gas, II: Many-$δ$ motions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912360104460288 |
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| author | Chen, Yu-Ting |
| author_facet | Chen, Yu-Ting |
| contents | This paper is the second 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. The main results here construct and study the more general stochastic many-$δ$ motions for $N$ particles. They have the interpretation of independent two-dimensional Brownian motions conditioned to attain the contact interactions that realize multiple two-body $δ$-function potentials. For the construction, we transform the stochastic one-$δ$ motions studied in [7] by Girsanov's theorem locally before a pair of particles with different initial conditions begins to contact each other. The strong Markov processes with lifetime thus obtained are concatenated by using the "no-triple-contacts" (NTC). This NTC phenomenon appears in the functional integral solutions of the two-dimensional many-body delta-Bose gas obtained earlier and is now proven at the pathwise level to a generalized degree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01704 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic motions of the two-dimensional many-body delta-Bose gas, II: Many-$δ$ motions Chen, Yu-Ting Probability This paper is the second 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. The main results here construct and study the more general stochastic many-$δ$ motions for $N$ particles. They have the interpretation of independent two-dimensional Brownian motions conditioned to attain the contact interactions that realize multiple two-body $δ$-function potentials. For the construction, we transform the stochastic one-$δ$ motions studied in [7] by Girsanov's theorem locally before a pair of particles with different initial conditions begins to contact each other. The strong Markov processes with lifetime thus obtained are concatenated by using the "no-triple-contacts" (NTC). This NTC phenomenon appears in the functional integral solutions of the two-dimensional many-body delta-Bose gas obtained earlier and is now proven at the pathwise level to a generalized degree. |
| title | Stochastic motions of the two-dimensional many-body delta-Bose gas, II: Many-$δ$ motions |
| topic | Probability |
| url | https://arxiv.org/abs/2505.01704 |