Stochastic motions of the two-dimensional many-body delta-Bose gas, IV: Transformations of relative motions

Abstract

This paper is the last in a series devoted to constructing stochastic motions representing the two-dimensional $N$-body delta-Bose gas for all integers $N\ge 3$ via Feynman-Kac-type formulas. The main result here supplements [1,2] of the series by proving a bijective transformation between two general classes of Langevin-type SDEs such that the SDEs of one class describe precisely the stochastic relative motions of the SDEs of the other class.

Replacement of the paper with the same arXiv identifier by part of its new version, 8 pages. The other parts of the new version appear as arXiv:2505.01703, arXiv:2505.01704, and arXiv:2505.03006