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pro vyhledávání: '"46L54"'
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:
Jeong, Yoonje, Youn, Sang-Gyun
We prove that a freer quantum group has smaller moments of the self-adjoint main character in the category of finitely generated discrete quantum groups. As a result, the moments are minimized pre-precisely by the unitary free quantum groups FU (Q).
Externí odkaz:
http://arxiv.org/abs/2411.11043
We prove that if $A_1, A_2, \dots, A_n$ are tracial abelian von Neumann algebras for $2\leq n \leq \infty$ and $M = A_1 * \cdots * A_n$ is their free product, then any subalgebra $A \subset M$ of the form $A = \sum_{i=1}^n u_i A_i p_i u_i^*$, for som
Externí odkaz:
http://arxiv.org/abs/2411.05136
Autor:
Chen, James, Olver, Sheehan
The Stieltjes (or sometimes called the Cauchy) transform is a fundamental object associated with probability measures, corresponding to the generating function of the moments. In certain applications such as free probability it is essential to comput
Externí odkaz:
http://arxiv.org/abs/2410.16178
A Gelfand-Tsetlin function is a real-valued function $\phi:C \to \mathbb{R}$ defined on a finite subset $C$ of the lattice $\mathbb{Z}^2$ with the property that $\phi(x) \leq \phi(y)$ for every edge $\langle x,y \rangle$ directed north or east betwee
Externí odkaz:
http://arxiv.org/abs/2410.10754
Autor:
Alt, Johannes, Krüger, Torben
We consider the Brown measure of $a+\mathfrak{c}$, where $a$ lies in a commutative tracial von Neumann algebra $\mathcal{B}$ and $\mathfrak{c}$ is a $\cal{B}$-valued circular element. Under certain regularity conditions on $a$ and the covariance of $
Externí odkaz:
http://arxiv.org/abs/2409.15405
Given a sequence of polynomials $Q_n$ of degree $n$, we consider the triangular table of derivatives $Q_{n, k}(x)=d^k Q_n(x) /d x^k$. Under the only assumption that the sequence $\{Q_n\}$ has a weak* limiting zero distribution (an empirical distribut
Externí odkaz:
http://arxiv.org/abs/2408.13851
We present a simplified explanation of why free fractional convolution corresponds to the differentiation of polynomials, by finding how the finite free cumulants of a polynomial behave under differentiation. This approach allows us to understand the
Externí odkaz:
http://arxiv.org/abs/2408.09337
We extend to arbitrary measures results of Bao, Erd\"os, Schnelli, Moreillon, and Ji on the connectedness of the supports of additive convolutions of measures on \mathbb{R} and of free multiplicative convolutions of measures on \mathbb{R}_+. More pre
Externí odkaz:
http://arxiv.org/abs/2408.06573
Higher-order notions of Kreweras complementation have appeared in the literature in the works of Krawczyk, Speicher, Mastnak, Nica, Arizmendi, Vargas, and others. While the theory has been developed primarily for specific applications in free probabi
Externí odkaz:
http://arxiv.org/abs/2407.17660