ALGEBRAIC COMBINATORICS

no. 6
Cyclic independence: Boolean and monotone
Arizmendi, Octavio1; Hasebe, Takahiro2; Lehner, Franz3
1 Centro de Investigación en Matemáticas. Calle Jalisco SN. Guanajuato, Mexico
2 Department of Mathematics, Hokkaido University, North 10 West 8, Kita-Ku, Sapporo 060-0810, Japan.
3 Institut für Diskrete Mathematik, Technische Universität Graz Steyrergasse 30, 8010 Graz, Austria
Algebraic Combinatorics, Volume 6 (2023) no. 6, pp. 1697-1734.

The present paper introduces a modified version of cyclic-monotone independence which originally arose in the context of random matrices, and also introduces its natural analogy called cyclic-Boolean independence. We investigate formulas for convolutions, limit theorems for sums of independent random variables, and also classify infinitely divisible distributions with respect to cyclic-Boolean convolution. Finally, we provide applications to the eigenvalues of the adjacency matrices of iterated star products of graphs and also iterated comb products of graphs.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.309
Classification: 46L54, 05C76
Keywords: Boolean independence, monotone independence, star product, comb product
Arizmendi, Octavio 1; Hasebe, Takahiro 2; Lehner, Franz 3

1 Centro de Investigación en Matemáticas. Calle Jalisco SN. Guanajuato, Mexico
2 Department of Mathematics, Hokkaido University, North 10 West 8, Kita-Ku, Sapporo 060-0810, Japan.
3 Institut für Diskrete Mathematik, Technische Universität Graz Steyrergasse 30, 8010 Graz, Austria
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Arizmendi, Octavio; Hasebe, Takahiro; Lehner, Franz. Cyclic independence: Boolean and monotone. Algebraic Combinatorics, Volume 6 (2023) no. 6, pp. 1697-1734. doi : 10.5802/alco.309. https://alco.centre-mersenne.org/articles/10.5802/alco.309/

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