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Abstract: We define a product of algebraic probability spaces equipped with two states.This product is called a conditionally monotone product. This product is a newexample of independence in non-commutative probability theory and unifies themonotone and Boolean products, and moreover, the orthogonal product. Then wedefine the associated cumulants and calculate the limit distributions incentral limit theorem and Poisson-s law of small numbers. We also prove acombinatorial moment-cumulant formula using monotone partitions. We investigatesome other topics such as infinite divisibility for the additive convolutionand deformations of the monotone convolution. We define cumulants for a generalconvolution to analyze the deformed convolutions.



Autor: Takahiro Hasebe

Fuente: https://arxiv.org/



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