| Autor: |
Bozejko, Marek, Bozejko, Wojciech |
| Rok vydání: |
2013 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
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 $S(\infty)=\bigcup S(n)$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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