Zobrazeno 1 - 10
of 907
pro vyhledávání: '"46L53"'
Autor:
Jekel, David
We study the interaction between entropy and Wasserstein distance in free probability theory. In particular, we give lower bounds for several versions of free entropy dimension along Wasserstein geodesics, as well as study their topological propertie
Externí odkaz:
http://arxiv.org/abs/2501.00703
This paper investigates additive processes with respect to several different independences in non-commutative probability in terms of the convolution hemigroups of the distributions of the increments of the processes. In particular, we focus on the r
Externí odkaz:
http://arxiv.org/abs/2412.18742
We describe all Gaussian generating functionals on several easy quantum groups given by non-crossing partitions. This includes in particular the free unitary, orthogonal and symplectic quantum groups. We further characterize central Gaussian generati
Externí odkaz:
http://arxiv.org/abs/2412.00595
The first paper in this series introduced a new approach to strong convergence of random matrices that is based primarily on soft arguments. This method was applied to achieve a refined qualitative and quantitative understanding of strong convergence
Externí odkaz:
http://arxiv.org/abs/2412.00593
Autor:
Díaz, Mario, Jaramillo, Arturo
We present a straightforward formulation of Stein's method for the semicircular distribution, specifically designed for the analysis of non-commutative random variables. Our approach employs a non-commutative version of Stein's heuristic, interpolati
Externí odkaz:
http://arxiv.org/abs/2411.16103
In the present paper, we develop the random restriction method in the quantum framework. By applying this method, we establish the quantum Eldan-Gross inequality, the quantum Talagrand isoperimetric inequality, and related quantum KKL-type inequaliti
Externí odkaz:
http://arxiv.org/abs/2411.12399
Autor:
Defant, Colin, Lee, Mitchell
Defant found that the relationship between a sequence of (univariate) classical cumulants and the corresponding sequence of (univariate) free cumulants can be described combinatorially in terms of families of binary plane trees called troupes. Using
Externí odkaz:
http://arxiv.org/abs/2409.05219
Autor:
Jorgensen, Palle E. T., Tian, James
Motivated by questions in quantum theory, we study Hilbert space valued Gaussian processes, and operator-valued kernels, i.e., kernels taking values in B(H) (= all bounded linear operators in a fixed Hilbert space H). We begin with a systematic study
Externí odkaz:
http://arxiv.org/abs/2408.10254
This article introduces operator on operator regression in quantum probability. Here in the regression model, the response and the independent variables are certain operator valued observables, and they are linearly associated with unknown scalar coe
Externí odkaz:
http://arxiv.org/abs/2408.00289
We study mixtures of free, monotone, and boolean independence described by directed graphs (digraphs). For a sequence of digraphs $G_n = (V_n,E_n)$, we give sufficient conditions for the limit $\widehat{\mu} = \lim_{n \to \infty} \boxplus_{G_n}(\mu_n
Externí odkaz:
http://arxiv.org/abs/2407.02276