arXiv 2401.005182024-01math.PRmath-phmath.CAmath.FAmath.MP

具有合流超几何核的行列式点过程的Palm层级，以及无限维酉群上调和分析问题中的分解测度

A Palm hierarchy for determinantal point processes with the confluent hypergeometric kernel, the decomposing measures in the problem of harmonic analysis on the infinite-dimensional unitary group

Alexander I. Bufetov

备注：: 23 pages

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AI总结：

本文证明无限维酉群调和分析中分解测度参数平移1等价于取无穷远约化Palm测度，通过正交多项式系综的有限维近似及Palm测度与标度极限的交换性完成证明。

摘要：

本文的主要结果是：在无限维酉群上调和分析问题中，分解测度参数空间中参数平移1，对应于对这些分解测度取无穷远处的约化Palm测度。证明过程通过正交多项式系综对测度进行有限维近似来完成。关键观察在于，取约化Palm测度这一操作与从有限粒子系统到无限粒子系统的标度极限过渡是交换的。

英文摘要：

The main result of this note is that the shift of the parameter by 1 in the parameter space of decomposing measures in the problem of harmonic analysis on the infinite-dimensional unitary group corresponds to the taking of the reduced Palm measure at infinity for our decomposing measures. The proof proceeds by finite-dimensional approximation of our measures by orthogonal polynomial ensembles. The key remark is that the taking the reduced Palm measure commutes with the scaling limit transition from finite to infinite particle systems.

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