Cyclic independence: Boolean and monotone

Octavio Arizmendi, Takahiro Hasebe, Franz Lehner

Research output: Working paperPreprint


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.
Original languageEnglish
Number of pages34
Publication statusPublished - 31 Mar 2022


  • math.PR
  • math.OA
  • 46L54, 05C76


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