Results 21 to 30 of about 4,039 (94)

General Fractional Calculus, Evolution Equations, and Renewal Processes

, 2011
We develop a kind of fractional calculus and theory of relaxation and diffusion equations associated with operators in the time variable, of the form $(Du)(t)=\frac{d}{dt}\int\limits_0^tk(t-\tau)u(\tau)\,d\tau -k(t)u(0)$ where $k$ is a nonnegative ...
Kochubei, Anatoly N.
core   +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

On the t-Transformation of Free Convolution

Mathematics
The study of the stability of measure families under measure transformations, as well as the accompanying limit theorems, is motivated by both fundamental and applied probability theory and dynamical systems. Stability analysis tries to uncover invariant
Shokrya S. Alshqaq, Ohud A. Alqasem, Raouf Fakhfakh   +2 more
doaj   +1 more source

Notes on the Free Additive Convolution

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

Studies on Cauchy–Stieltjes Kernel Families

Mathematics
In the setting of Cauchy–Stieltjes kernel (CSK) families, this study provides some features of free Poisson, free Gamma, and free Binomial laws, as well as some innovative limit theorems linked to Fermi convolution.
Abdulmajeed Albarrak, Raouf Fakhfakh, Ghadah Alomani   +2 more
doaj   +1 more source

Spectral measure of heavy tailed band and covariance random matrices

, 2009
We study the asymptotic behavior of the appropriately scaled and possibly perturbed spectral measure $\mu$ of large random real symmetric matrices with heavy tailed entries.
A.M. Khorunzhy, Alice Guionnet, Amir Dembo, G. Ben Arous, I. Zakharevich, J. Bouchaud, S.B. Chae, Serban Belinschi, W. Bryc   +8 more
core   +3 more sources

Eigenvector dynamics under free addition

, 2014
We investigate the evolution of a given eigenvector of a symmetric (deterministic or random) matrix under the addition of a matrix in the Gaussian orthogonal ensemble.
Allez, Romain, Bouchaud, Jean-Philippe
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

Convolution powers in the operator-valued framework

, 2011
We consider the framework of an operator-valued noncommutative probability space over a unital C*-algebra B. We show how for a B-valued distribution \mu one can define convolution powers with respect to free additive convolution and with respect to ...
Anshelevich, Michael, Belinschi, Serban T., Fevrier, Maxime, Nica, Alexandru   +3 more
core   +3 more sources

r-Free Convolution and Variance Function

Axioms
The concept of r-free convolution (which is represented by r) was introduced for 0≤r≤1. It is equal to the Boolean additive convolution ⊎ if r=0 and reduced to the free additive convolution ⊞ when r=1.
Shokrya S. Alshqaq, Raouf Fakhfakh, Fatimah Alshahrani   +2 more
doaj   +1 more source