Generalized Gaussian processes and relations with random matrices and\n positive definite functions on permutation groups

2013/01/11 by Marek Bożejko, Bozejko, Marek, Wojciech Bożejko +1 · 1 citation
Computer Science · Mathematics · #05C30 #46L54 #Advanced Algebra and Geometry #Bayesian Methods and Mixture Models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1301.2502

openalex publication_date 2013/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main purpose of this paper of the paper is an explicite construction of\ngeneralized Gaussian process with function t_b(V)=b^H(V), where\nH(V)=n-h(V), h(V) is the number of singletons in a pair-partition V \∈\n stP₂(2n).\n This gives another proof of Theorem of A. Buchholtz citeBuch that t_b is\npositive definite function on the set of all pair-partitions.\n Some new combinatorial formulas are also presented. Connections with free\nadditive convolutions probability measure on \ℝ are also done. Also\nnew positive definite functions on permutations are presented and also it is\nproved that the function H is norm (on the group S(\∞)= bigcup S(n).\n

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