Cyclic independence: Boolean and monotone

Abstract

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.

34 pages; EU-logo added, no other changes

References in corpus (3)

• A new proof for the multiplicative property of the boolean cumulants with applications to operator-valued case
• Matrix models for cyclic monotone and monotone independences
• Freeness of type $B$ and conditional freeness for random matrices

Cited by in corpus (1)

• Matrix models for cyclic monotone and monotone independences