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

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arxiv 2401.17243 v3 pith:UIBLDZPV submitted 2024-01-30 math.PR

Yu-Ting Chen This is my paper · ORCID
classification math.PR
keywords motionssdesstochasticclassdelta-boserelativeseriestwo-dimensional
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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 $N\geq 3$ 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.

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  1. Sharp moment and upper tail asymptotics for the critical $2d$ Stochastic Heat Flow

    math.PR 2025-07 conditional novelty 8.0 of 10

    The h-th moment of the critical 2d Stochastic Heat Flow mass is at least exp(exp(c h)), matching a 1999 prediction and exponentially improving the known lower bound.

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