32 citations · 185 across the 24 of their papers we have counts for
29 papers
Noncommutative majorization
Matthew Kennedy, Paul Skoufranis
We introduce a theory of noncommutative majorization that extends the classical majorization theory introduced by Hardy, Littlewood and Pólya to tuples of self-adjoint matrices tha…
Central Limit Theorem for Tensor Products of Free Variables via Bi-Free Independence
Paul Skoufranis
In this paper, a connection between bi-free probability and the asymptotics of random quantum channels and tensor products of random matrices is established. Using bi-free matrix m…
Joint Majorization in Continuous Matrix Algebras
Xavier Mootoo, Paul Skoufranis
Various notions of joint majorization are examined in continuous matrix algebras. The relative strengths of these notions are established via proofs and examples. In addition, the…
Non-Commutative Stochastic Processes and Bi-Free Probability
Paul Skoufranis
In this paper, a connection between bi-free probability and the theory of non-commutative stochastic processes is examined. Specifically it is demonstrated that the transition oper…
Restricted invertibility of continuous matrix functions
Adrian Fan, Jack Montemurro, Pavlos Motakis +4
Motivated by an influential result of Bourgain and Tzafriri, we consider continuous matrix functions and lower -norm bounds associated with…
Bi-Free Entropy with Respect to Completely Positive Maps
Georgios Katsimpas, Paul Skoufranis
In this paper, a notion of non-microstate bi-free entropy with respect to completely positive maps is constructed thereby extending the notions of non-microstate bi-free entropy an…
Analogues of Entropy in Bi-Free Probability Theory: Microstates
Ian Charlesworth, Paul Skoufranis
In this paper, we extend the notion of microstate free entropy to the bi-free setting. In particular, using the bi-free analogue of random matrices, microstate bi-free entropy is d…
Analogues of Entropy in Bi-Free Probability Theory: Non-Microstate
Ian Charlesworth, Paul Skoufranis
In this paper, we extend the notion of non-microstate free entropy to the bi-free setting. Using a diagrammatic approach involving bi-non-crossing diagrams, bi-free difference quot…
Bi-monotonic independence for pairs of algebras
Yinzheng Gu, Takahiro Hasebe, Paul Skoufranis
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 n…
A Combinatorial Approach to the Opposite Bi-Free Partial -Transform
Paul Skoufranis
In this paper, we present a combinatorial approach to the opposite 2-variable bi-free partial -transforms where the opposite multiplication is used on the right. In addition, ex…
Bi-Boolean independence for pairs of algebras
Yinzheng Gu, Paul Skoufranis
In this paper, the notion of bi-Boolean independence for non-unital pairs of algebras is introduced thereby extending the notion of Boolean independence to pairs of algebras. The n…
Analytic subordination for bi-free convolution
Serban Belinschi, Hari Bercovici, Yinzheng Gu +1
In this paper we study some analytic properties of bi-free additive convolution, both scalar and operator-valued. We show that using properties of Voiculescu's subordination functi…
Conditionally Bi-Free Independence with Amalgamation
Yinzheng Gu, Paul Skoufranis
In this paper, we introduce the notion of conditionally bi-free independence in an amalgamated setting. We define operator-valued conditionally bi-multiplicative pairs of functions…
Conditionally Bi-Free Independence for Pairs of Algebras
Yinzheng Gu, Paul Skoufranis
In this paper, the notion of conditionally bi-free independence for pairs of algebras is introduced. The notion of conditional -cumulants are introduced and it is demons…
Majorization in C*-algebras
Ping Wong Ng, Leonel Robert, Paul Skoufranis
We investigate the closed convex hull of unitary orbits of selfadjoint elements in arbitrary unital C*-algebras. Using a notion of majorization against unbounded traces, a characte…
Closed convex hulls of unitary orbits in certain simple real rank zero C-algebras
Ping Wong Ng, Paul Skoufranis
In this paper, we characterize the closures of convex hulls of unitary orbits of self-adjoint operators in unital, separable, simple C-algebras with non-trivial tracial simplex…
On Operator-Valued Bi-Free Distributions
Paul Skoufranis
In this paper, operator-valued bi-free distributions are investigated. Given a subalgebra of a unital algebra , it is established that a two-faced family is bi-free from…
Some Bi-Matrix Models for Bi-Free Limit Distributions
Paul Skoufranis
In this paper, an analogue of matrix models from free probability is developed in the bi-free setting. A bi-matrix model is not simply a pair of matrix models, but a pair of matrix…
A Combinatorial Approach to Voiculescu's Bi-Free Partial Transforms
Paul Skoufranis
In this paper, we present a combinatorial approach to the 2-variable bi-free partial - and -transforms recently discovered by Voiculescu. This approach produces an alternate…
Closed Convex Hulls of Unitary Orbits in C-Algebras of Real Rank Zero
Paul Skoufranis
In this paper, we study closed convex hulls of unitary orbits in various C-algebras. For unital C-algebras with real rank zero and a faithful tracial state determining equi…
Numerical Ranges in II Factors
Ken Dykema, Paul Skoufranis
In this paper, we generalize the notion of the -numerical range of a matrix to operators in arbitrary tracial von Neumann algebras. For each self-adjoint operator , the -n…
Independences and Partial -Transforms in Bi-Free Probability
Paul Skoufranis
In this paper, we examine how various notions of independence in non-commutative probability theory arise in bi-free probability. We exhibit how Boolean and monotone independence o…
Combinatorics of Bi-Freeness with Amalgamation
Ian Charlesworth, Brent Nelson, Paul Skoufranis
In this paper, we develop the theory of bi-freeness in an amalgamated setting. We construct the operator-valued bi-free cumulant functions, and show that the vanishing of mixed cum…
Thompson's theorem for II_1 factors
Matthew Kennedy, Paul Skoufranis
A theorem of Thompson provides a non-self-adjoint variant of the classical Schur-Horn theorem by characterizing the possible diagonal values of a matrix with given singular values.…