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Generalized Gaussian processes and relations with random matrices and positive definite functions on permutation groups
- Publication Year :
- 2013
-
Abstract
- The main purpose of this paper of the paper is an explicite construction of generalized Gaussian process with function $t_b(V)=b^{H(V)}$, where $H(V)=n-h(V)$, $h(V)$ is the number of singletons in a pair-partition $V \in \st{P}_2(2n)$. This gives another proof of Theorem of A. Buchholtz \cite{Buch} that $t_b$ is positive definite function on the set of all pair-partitions. Some new combinatorial formulas are also presented. Connections with free additive convolutions probability measure on $\mathbb{R}$ are also done. Also new positive definite functions on permutations are presented and also it is proved that the function $H$ is norm (on the group $S(\infty)=\bigcup S(n)$.
- Subjects :
- Mathematics - Probability
Mathematical Physics
46L54, 05C30
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1301.2502
- Document Type :
- Working Paper