On operator-valued infinitesimal Boolean and monotone independence
نویسندگان
چکیده
We introduce the notion of operator-valued infinitesimal (OVI) independence for Boolean and monotone cases. Then show that OVI (resp. monotone) is equivalent to over an algebra $2\times 2$ upper triangular matrices. Moreover, we derive formulas obtain additive convolution by reducing it case. also define cumulants study its basic properties. each independence, construct corresponding Central Limit Theorem. The relations among free, are extended this setting. Besides, in case deduce vanishing mixed still use connect scalar-valued with matrix-valued independence. Finally two random matrix models asymptotically independent but turn out not be infinitesimally independent.
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ژورنال
عنوان ژورنال: Infinite Dimensional Analysis, Quantum Probability and Related Topics
سال: 2021
ISSN: ['0219-0257', '1793-6306']
DOI: https://doi.org/10.1142/s0219025721500193