Marchenko–pastur law - Open Access .click

Results 21 to 30 of about 5,585,535 (119)

Axioms
The 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, Raouf Fakhfakh, Fatimah Alshahrani +2 more
doaj +1 more source

Stability of Cauchy–Stieltjes Kernel Families by Free and Boolean Convolutions Product

Mathematics
Let 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, Shokrya S. Alshqaq, Raouf Fakhfakh +2 more
doaj +1 more source

Distributions on an Interval as a Scale-Invariant Combination of Scale-Invariant Functions: Theoretical Explanation of Empirical Marchenko-Pastur-Type Distributions [PDF]

, 2021
In many practical situations, we know the lower and upper bounds L and U on possible values of a quantity x. In such situations, the probability distribution of this quantity is also located on the corresponding interval [L, U].
Le, Chon Van, Kreinovich, Vladik, Alvarez, Kevin +2 more
core +1 more source

Covariance Estimation for Wide Data

WIREs Computational Statistics, Volume 18, Issue 2, June 2026.
Covariance matrix estimation is fundamental to multivariate analysis, with applications spanning finance, genomics, climate science, and signal processing. This review synthesizes recent advances in high‐dimensional covariance estimation‐thresholding, linear and nonlinear shrinkage, graphical models, and random matrix theory‐under a unifying framework ...
Eran Raviv
wiley +1 more source

A total positivity property of the Marchenko-Pastur Law

, 2015
A property of the Marchenko-Pastur measure related to total positivity is presented. The theoretical results are applied to the accurate computation of the roots of the corresponding orthogonal polynomials, an important issue in the construction of ...
Martinez, Jose-Javier, Marco, Ana
core +1 more source

V_a-Deformed Free Convolution

Mathematics
In 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
doaj +1 more source

Free energy expansions of a conditional GinUE and large deviations of the smallest eigenvalue of the LUE

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, Seong‐Mi Seo, Meng Yang +2 more
wiley +1 more source

In Vivo Characterization of Magnetic Inclusions in the Subcortex From Nonexponential Transverse Relaxation Decay

NMR in Biomedicine, Volume 38, Issue 6, June 2025.
Nonexponential transverse relaxation decay allows to characterize the spatial distribution of magnetic material within subcortical grey matter tissue. ABSTRACT According to theoretical studies, MRI signal decay due to transverse relaxation in brain tissue with magnetic inclusions (e.g., blood vessels and iron‐rich cells) is expected to follow a ...
Rita Oliveira +5 more
wiley +1 more source

Wigner- and Marchenko-Pastur-type limits for Jacobi processes [PDF]

, 2022
We study Jacobi processes $(X_{t})_{t\ge0}$ on the compact spaces $[-1,1]^N$ and on the noncompact spaces $[1,\infty[^N$ which are motivated by the Heckman-Opdam theory for the root systems of type BC and associated integrable particle systems.
Auer, Martin +2 more
core +1 more source

Linear regression with weak exogeneity

Quantitative Economics, Volume 16, Issue 2, Page 367-403, May 2025.
This paper studies linear time‐series regressions with many regressors. Weak exogeneity is the most used identifying assumption in time series. Weak exogeneity requires the structural error to have zero conditional expectation given present and past regressor values, allowing errors to correlate with future regressor realizations.
Anna Mikusheva, Mikkel Sølvsten
wiley +1 more source

variance function
cauchy–stieltjes transform
random matrix theory