Airy point process via supersymmetric lifts
Airy point process via supersymmetric lifts
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通过超对称提升的艾里点过程
DOI：
10.2140/pmp.2022.3.869
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Andrew Ahn
中科院分区：
文献类型：
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作者：
Andrew Ahn
对称函数的超对称提升是一个特殊的双对称提升序列，它满足序列中相邻提升之间的抵消性质。我们得到的轮廓积分公式的粒子系统的可观的超对称升降机的某些相关的生成函数。我们还得到了多元Bessel函数和Schur函数的一族超对称提升，沿着给出了它们的围道积分公式。这些公式是服从局部渐近的极值边缘的粒子系统所产生的酉不变的随机矩阵和分解的酉群的表示。我们专注于几个设置中出现的艾里点过程。
A supersymmetric lift of a symmetric function is a special sequence of doubly symmetric lifts which satisfies a cancellation property relating neighboring lifts in the sequence. We obtain contour integral formulas for observables of particle systems in terms of supersymmetric lifts of certain associated generating functions. We also obtain a family of supersymmetric lifts of multivariate Bessel functions and of Schur functions, along with contour integral formulas them. These formulas are amenable to local asymptotics at the extremal edge of particle systems arising from unitarily invariant random matrices and decompositions of representations of the unitary group. We focus on several settings where the Airy point process arises.