Results 31 to 40 of about 3,271,458 (133)
Studies on the Marchenko–Pastur Law
MathematicsIn free probability, the theory of Cauchy–Stieltjes Kernel (CSK) families has recently been introduced. This theory is about a set of probability measures defined using the Cauchy kernel similarly to natural exponential families in classical probability ...
Ayed. R. A. Alanzi +3 more
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International Journal of Innovative Research in EngineeringThis paper introduces a novel framework of creatively equipped convex topological spaces to address challenges in theoretical forward models. We extend the Gelfand–Shilov technique to generalize the Laplace–Stieltjes transform via a simple objective ...
P. G.
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Some Results on the Free Poisson Distribution
AxiomsLet K+(μi)={Qsiμi,si∈(m0μi,m+μi)}, i=1,2, be two CSK families generated by the nondegenerate probability measures μ1 and μ2 with support bounded from above.
Ayed. R. A. Alanzi +3 more
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Edge Density Expansions for the Classical Gaussian and Laguerre Ensembles
Studies in Applied Mathematics, Volume 157, Issue 3, September 2026.ABSTRACT Recent work of Bornemann has uncovered hitherto hidden integrable structures relating to the asymptotic expansion of quantities at the soft edge of the Gaussian and Laguerre random matrix ensembles. These quantities are spacing distributions and the eigenvalue density, and the findings cover the cases of the three symmetry classes: orthogonal,
Peter J. Forrester +2 more
wiley +1 more source
Central Limit Theorem for V-Monotone Independence
Complex Analysis and Operator TheoryWe study the distribution μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}
Adrian Dacko
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One‐level densities in families of Grössencharakters associated to CM elliptic curves
Mathematika, Volume 72, Issue 1, January 2026.Abstract We study the low‐lying zeros of a family of L$L$‐functions attached to the complex multiplication elliptic curve Ed:y2=x3−dx$E_d \;:\; y^2 = x^3 - dx$, for each odd and square‐free integer d$d$. Specifically, upon writing the L$L$‐function of Ed$E_d$ as L(s−12,ξd)$L(s-\frac{1}{2}, \xi _d)$ for the appropriate Grössencharakter ξd$\xi _d$ of ...
Chantal David, Lucile Devin, Ezra Waxman
wiley +1 more source
On
MathematicsThe concept of the (T=(s,t))-transformation of probability measures, introduced for s>0 and t∈R, is examined in this work from the perspective of Cauchy–Stieltjes kernel (CSK) families and their related variance functions (VFs).
Shokrya S. Alshqaq +2 more
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On a New Extension of the t-Transformation of Probability Measures
SymmetryThis paper establishes a comprehensive analytical framework for a new transformation of probability measures, denoted by T(a,t), which unifies the classical t- and Ta-transformations in free probability. We derive the functional equation characterizing T(
Abdulmajeed Albarrak +2 more
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Abstract and Applied Analysis, Volume 2026, Issue 1, 2026.This paper investigates the stability of an Euler–Bernoulli beam subject to boundary memory and highlights the fundamentally different mechanisms associated with polynomially and exponentially decaying resolvent kernels. The formulation distinguishes the original memory kernel, its Volterra resolvent, the compatibility conditions, and the corresponding
Marie Esther Anassé +3 more
wiley +1 more source
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
doaj +1 more source