Bi-monotonic independence for pairs of algebras
Operator Algebras
2021-06-25 v5 Probability
Abstract
In this article, the notion of bi-monotonic independence is introduced as an extension of monotonic independence to the two-faced framework for a family of pairs of algebras in a non-commutative space. The associated cumulants are defined and a moment-cumulant formula is derived in the bi-monotonic setting. In general the bi-monotonic product of states is not a state and the bi-monotonic convolution of probability measures on the plane is not a probability measure. This provides an additional example of how positivity need not be preserved under conditional bi-free convolutions.
Keywords
Cite
@article{arxiv.1708.05334,
title = {Bi-monotonic independence for pairs of algebras},
author = {Yinzheng Gu and Takahiro Hasebe and Paul Skoufranis},
journal= {arXiv preprint arXiv:1708.05334},
year = {2021}
}
Comments
accepted by Journal of Theoretical Probability