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of 1 448
pro vyhledávání: '"46L54"'
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 $\mathcal{B}$-valued circular element. Under certain regularity conditions on $a$ and the covariance
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
Autor:
Mingo, James A., George, Daniel Munoz
We compute the fluctuation moments $\alpha_{m_1,\dots,m_r}$ of a Complex Wigner Matrix $X_N$ given by the limit $\lim_{N\rightarrow\infty}N^{r-2}k_r(Tr(X_N^{m_1}),\dots,Tr(X_N^{m_r}))$. We prove the limit exists and characterize the leading order via
Externí odkaz:
http://arxiv.org/abs/2407.17608
Autor:
Neufeld, Leonie
We show that the distribution of self-normalized sums of free self-adjoint random variables converges weakly to Wigner's semicircle law under appropriate conditions and estimate the rate of convergence in terms of the Kolmogorov distance. In the case
Externí odkaz:
http://arxiv.org/abs/2406.13601
The first paper in this series introduced a new family of nonasymptotic matrix concentration inequalities that sharply capture the spectral properties of very general Gaussian (as well as non-Gaussian) random matrices in terms of an associated noncom
Externí odkaz:
http://arxiv.org/abs/2406.11453