Results 31 to 40 of about 3,040,184 (131)
Local law for random Gram matrices [PDF]
, 2016 We prove a local law in the bulk of the spectrum for random Gram matrices XX∗, a generalization of sample covariance matrices, where X is a large matrix with independent, centered entries with arbitrary variances.
J. Alt, L'aszl'o ErdHos, T. Kruger
semanticscholar +1 more source
Marchenko–Pastur Law for Spectra of Random Weighted Bipartite Graphs
Siberian Advances in MathematicsWe study the spectra of random weighted bipartite graphs. We establish that, under specific assumptions on the edge probabilities, the symmetrized empirical spectral distribution function of the graph’s adjacency matrix converges to the symmetrized ...
A. V. Nadutkina +2 more
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Notes on the Free Additive Convolution
AxiomsThe investigation of free additive convolution is a key concept in free probability theory, offering a framework for studying the sum of freely independent random variables.
Shokrya S. Alshqaq +2 more
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Spectral density of generalized Wishart matrices and free multiplicative convolution
, 2015 We investigate the level density for several ensembles of positive random matrices of a Wishart--like structure, $W=XX^{\dagger}$, where $X$ stands for a nonhermitian random matrix.
A. Nica +13 more
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Stability of Cauchy–Stieltjes Kernel Families by Free and Boolean Convolutions Product
MathematicsLet F(νj)={Qmjνj,mj∈(m−νj,m+νj)}, j=1,2, be two Cauchy–Stieltjes Kernel (CSK) families induced by non-degenerate compactly supported probability measures ν1 and ν2. Introduce the set of measures F=F(ν1)⊞F(ν2)={Qm1ν1⊞Qm2ν2,m1∈(m−ν1,m+ν1)andm2∈(m−ν2,m+ν2)}.
Ayed. R. A. Alanzi +2 more
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On the Spectral Norms of Pseudo-Wigner and Related Matrices
, 2017 We investigate the spectral norms of symmetric $N \times N$ matrices from two pseudo-random ensembles. The first is the pseudo-Wigner ensemble introduced in "Pseudo-Wigner Matrices" by Soloveychik, Xiang and Tarokh and the second is its sample covariance-
Soloveychik, Ilya, Tarokh, Vahid
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Communications on Pure and Applied Mathematics, Volume 78, Issue 12, Page 2247-2304, December 2025.Abstract We consider a planar Coulomb gas ensemble of size N$N$ with the inverse temperature β=2$\beta =2$ and external potential Q(z)=|z|2−2clog|z−a|$Q(z)=|z|^2-2c \log |z-a|$, where c>0$c>0$ and a∈C$a \in \mathbb {C}$. Equivalently, this model can be realised as N$N$ eigenvalues of the complex Ginibre matrix of size (c+1)N×(c+1)N$(c+1) N \times (c+1)
Sung‐Soo Byun +2 more
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MathematicsIn this article, we study Va-transformation of a measure and of a convolution (denoted by a) defined for a∈R. We provide significant insights into the stability of the free Meixner family of probability measures under Va-transformation.
Fahad Alsharari, Raouf Fakhfakh
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Product of Ginibre matrices: Fuss-Catalan and Raney distributions
, 2011 Squared singular values of a product of s square random Ginibre matrices are asymptotically characterized by probability distribution P_s(x), such that their moments are equal to the Fuss-Catalan numbers or order s.
Penson, Karol A., Zyczkowski, Karol
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Marchenko-Pastur Theorem and Bercovici-Pata bijections for heavy-tailed or localized vectors [PDF]
, 2012 The celebrated Marchenko-Pastur theorem gives the asymptotic spectral distribution of sums of random, independent, rank-one projections. Its main hypothesis is that these projections are more or less uniformly distributed on the first grassmannian, which
Benaych-Georges, Florent +1 more
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