AI 中文总结
该研究建立Jack-Plancherel过程的多时间软边矩收敛性，推导其极限矩的布朗桥展开，确定等时极限与Airy_β过程的关联，得到边际b猜想的渐近β拓扑展开及β=2时Witten-Kontsevich相交数的显式非负公式。
AI 中文摘要
对于所有β>0，我们建立了Jack-Plancherel过程的多时间软边矩收敛性，该过程是Dyson布朗运动的离散β类比。极限矩可表示为非负布朗桥的绝对收敛展开，这类布朗桥由一对大小相等、方向相反的跳跃修饰。在等时情况下，我们确定该极限对应β≥1时Airy_β过程的联合拉普拉斯统计量。同样的布朗展开还给出了边际b猜想的渐近β拓扑展开，且在β=2时，得到了Witten-Kontsevich相交数的显式非负公式。
英文摘要
For every $β>0$, we establish multi-time soft-edge moment convergence for 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.
Comments64 pages, 3 figures
