Stochastic motions of the two-dimensional many-body delta-Bose gas, III: Path integrals

Yu-Ting Chen

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arXiv · 2505.03006

Stochastic motions of the two-dimensional many-body delta-Bose gas, III: Path integrals

Yu-Ting Chen

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Abstract

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-$\delta$ 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.

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Yu-Ting Chen. 2025-05-05. Stochastic motions of the two-dimensional many-body delta-Bose gas, III: Path integrals. https://arxiv.org/abs/2505.03006

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