Geodesic
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, Tome 6 (2023) no. 6, pp. 1697-1734

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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.

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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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Cyclic independence: {Boolean} and monotone},
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Arizmendi, Octavio; Hasebe, Takahiro; Lehner, Franz. Cyclic independence: Boolean and monotone. Algebraic Combinatorics, Tome 6 (2023) no. 6, pp. 1697-1734. doi: 10.5802/alco.309

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