Zobrazeno 1 - 10
of 97
pro vyhledávání: '"SKOUFRANIS, PAUL"'
Autor:
Skoufranis, Paul
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 models, it is demonstrated that the spectral distribution of certain se
Externí odkaz:
http://arxiv.org/abs/2405.19216
Autor:
Mootoo, Xavier, Skoufranis, Paul
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 closed convex hulls of joint unitary orbits are completely characteriz
Externí odkaz:
http://arxiv.org/abs/2210.13309
Autor:
Skoufranis, Paul
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 operators for non-commutative stochastic processes can be modelled using t
Externí odkaz:
http://arxiv.org/abs/2204.11636
Autor:
Fan, Adrian, Montemurro, Jack, Motakis, Pavlos, Praveen, Naina, Rusonik, Alyssa, Skoufranis, Paul, Tobin, Noam
Motivated by an influential result of Bourgain and Tzafriri, we consider continuous matrix functions $A:\mathbb{R}\to M_{n\times n}$ and lower $\ell_2$-norm bounds associated with their restriction to certain subspaces. We prove that for any such $A$
Externí odkaz:
http://arxiv.org/abs/2201.04238
Autor:
Katsimpas, Georgios, Skoufranis, Paul
Publikováno v:
Can. J. Math.-J. Can. Math. 76 (2024) 1163-1239
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 and free entropy with respect to a completely positive map. By extending
Externí odkaz:
http://arxiv.org/abs/2106.13114
Autor:
Charlesworth, Ian, Skoufranis, Paul
Publikováno v:
International Mathematics Research Notices, 2021; rnab279
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 defined. Properties essential to an entropy theory are developed, such
Externí odkaz:
http://arxiv.org/abs/1902.03874
Autor:
Charlesworth, Ian, Skoufranis, Paul
Publikováno v:
Advances in Mathematics 375 (2020), 107367
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 quotients are constructed as analogues of the free partial derivations. Ad
Externí odkaz:
http://arxiv.org/abs/1902.03873
Publikováno v:
Journal of Theoretical Probability 33 (2020), 533-566
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 momen
Externí odkaz:
http://arxiv.org/abs/1708.05334
Autor:
Skoufranis, Paul
Publikováno v:
Operators and Matrices 12 (2018), no. 2, 333-355
In this paper, we present a combinatorial approach to the opposite 2-variable bi-free partial $S$-transforms where the opposite multiplication is used on the right. In addition, extensions of this partial $S$-transforms to the conditional bi-free and
Externí odkaz:
http://arxiv.org/abs/1705.02857
Autor:
Gu, Yinzheng, Skoufranis, Paul
Publikováno v:
Complex Analysis and Operator Theory 13 (2019), no. 7, 3023-3089
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 notion of B-$(\ell, r)$-cumulants is defined via a bi-Boolean moment-cu
Externí odkaz:
http://arxiv.org/abs/1703.03072