Cyclic independence: Boolean and monotone
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929364637057024 |
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| author | Arizmendi, Octavio Hasebe, Takahiro Lehner, Franz |
| author_facet | Arizmendi, Octavio Hasebe, Takahiro Lehner, Franz |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_00072 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Cyclic independence: Boolean and monotone Arizmendi, Octavio Hasebe, Takahiro Lehner, Franz Probability Operator Algebras 46L54, 05C76 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. |
| title | Cyclic independence: Boolean and monotone |
| topic | Probability Operator Algebras 46L54, 05C76 |
| url | https://arxiv.org/abs/2204.00072 |