03.X.2023
James A. Mingo, Queen's University, Kingston, Canada
"Infinitesimal Operators"
Abstract: Motivated by signal plus noise models, we introduce the concept of an infinitesimal operator. This is an operator that can only be detected at one order lower than the ambient order, as in the joint distribution of a fixed finite rank tantric and a large random matrix. In our model infinitesimal operators have a strong form of independence from 'regular' operators. We show how the distributions of the commutator and anti-commutator of a 'regular' and infinitesimal operator can easily be computed and we show that infinitesimal operators make a connection between free and Boolean independence. This is joint work with Pei-Lun Tseng (NYU Abu Dhabi).
James A. Mingo, Queen's University, Kingston, Canada
"Infinitesimal Operators"
Abstract: Motivated by signal plus noise models, we introduce the concept of an infinitesimal operator. This is an operator that can only be detected at one order lower than the ambient order, as in the joint distribution of a fixed finite rank tantric and a large random matrix. In our model infinitesimal operators have a strong form of independence from 'regular' operators. We show how the distributions of the commutator and anti-commutator of a 'regular' and infinitesimal operator can easily be computed and we show that infinitesimal operators make a connection between free and Boolean independence. This is joint work with Pei-Lun Tseng (NYU Abu Dhabi).
Everyone is cordially invited!
B. Kołodziejek, W. Matysiak, K. Szpojankowski, J. Wesołowski