Year: 2026
Type: preprint
Abstract: For every $β>0$, we establish multi-time soft-edge moment convergence for a class of Jack processes, including the Jack--Plancherel process, a discrete $β$-analogue of Dyson Brownian motion. The limiting moments admit an absolutely convergent expansion in terms of nonnegative Brownian bridges decorated by pairs of equal and opposite jumps. At equal times, we identify this limit with the joint Laplace statistics of the Airy$_β$ process for $β\geq1$. The same Brownian expansion yields an asymptotic $β$-topological expansion of the marginal $b$-conjecture and, at $β=2$, an explicit nonnegative formula for the Witten--Kontsevich intersection numbers.
Source: arXiv (Cornell University)
Author: Xu, Jiaming
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208777205