论文标题
通过超对称升降机通风的点过程
Airy Point Process via Supersymmetric Lifts
论文作者
论文摘要
我们研究了以下粒子系统的局部渐近学，该粒子系统由以下粒子系统产生：（i）单位不变的随机遗传矩阵总和和（ii）对应于统一组表示的张量产物的签名。我们的方法并行处理这两个模型，并基于根据特殊的升力系列所描述的新公式，我们称之为超对称性升力，Schur函数和多元贝塞尔功能。我们获得了受\ cite {MJ03}启发的超对称Schur函数的确定性公式启发的一类超对称升力的明确表达式。对这些升力的渐近分析使我们能够探测边缘。我们专注于几种出现通风过程的设置。
We study the local asymptotics at the edge for particle systems arising from: (i) eigenvalues of sums of unitarily invariant random Hermitian matrices and (ii) signatures corresponding to decompositions of tensor products of representations of the unitary group. Our method treats these two models in parallel, and is based on new formulas for observables described in terms of a special family of lifts, which we call supersymmetric lifts, of Schur functions and multivariate Bessel functions. We obtain explicit expressions for a class of supersymmetric lifts inspired by determinantal formulas for supersymmetric Schur functions due to \cite{MJ03}. Asymptotic analysis of these lifts enable us to probe the edge. We focus on several settings where the Airy point process arises.
