Stochastic motions of the two-dimensional many-body delta-Bose gas, III: Path integrals
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908351459229696 |
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| author | Chen, Yu-Ting |
| author_facet | Chen, Yu-Ting |
| contents | This paper is the third 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 prove the Feynman-Kac-type formulas by using the stochastic many-$δ$ motions from [7] as the underlying diffusions. The associated multiplicative functionals show a new form and are derived from the analytic solutions of the two-dimensional $N$-body delta-Bose gas obtained in [4]. For completeness, the main theorem includes the formula for $N=2$, which is a minor modification of the Feynman--Kac-type formula proven in [5] for the relative motions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03006 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic motions of the two-dimensional many-body delta-Bose gas, III: Path integrals Chen, Yu-Ting Probability This paper is the third 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 prove the Feynman-Kac-type formulas by using the stochastic many-$δ$ motions from [7] as the underlying diffusions. The associated multiplicative functionals show a new form and are derived from the analytic solutions of the two-dimensional $N$-body delta-Bose gas obtained in [4]. For completeness, the main theorem includes the formula for $N=2$, which is a minor modification of the Feynman--Kac-type formula proven in [5] for the relative motions. |
| title | Stochastic motions of the two-dimensional many-body delta-Bose gas, III: Path integrals |
| topic | Probability |
| url | https://arxiv.org/abs/2505.03006 |