Results 1 to 10 of about 2,499,569 (102)

On Generalized V_a-Transformation of Measures

Mathematics
In this study, we introduce a novel transformation of probability measures that unifies two significant transformations in free probability theory: the t-transformation and the Va-transformation.
Abdulmajeed Albarrak, Raouf Fakhfakh, Ghadah Alomani   +2 more
doaj   +2 more sources

Some class of nonlinear partial differential equations in the ring of copolynomials over a commutative ring

Frontiers in Applied Mathematics and Statistics
We study the copolynomials, i.e., K-linear mappings from the ring of polynomials K[x] into the commutative ring K. With the help of the Cauchy–Stieltjes transform of a copolynomial, we introduce and examine a multiplication of copolynomials.
Sergiy L. Gefter, Aleksey L. Piven'
doaj   +2 more sources

A Generalized Framework for the (a, b)-Transformation of Probability Measures

Mathematics
In this paper, we propose an analytic deformation acting on probability measures, designed to encompass and extend two fundamental operators in free probability: the (a,b)- and the Tc-deformations.
Raouf Fakhfakh, Ghadah Alomani, Abdulmajeed Albarrak   +2 more
doaj   +2 more sources

A Common Generalization of the (a,b)- and (s,t)-Transformations of Probability Measures

Axioms
This paper presents two analytic mappings defined on probability measures that extend and unify the (a,b)- and (s,t)-deformations arising in free probability for s, b>0 and a, t∈R.
Ghadah Alomani, Raouf Fakhfakh
doaj   +2 more sources

Random matrices associated to Young diagrams [PDF]

Random Matrices. Theory and Applications, 2023
We consider the singular values of certain Young diagram shaped random matrices. For block-shaped random matrices, the empirical distribution of the squares of the singular eigenvalues converges almost surely to a distribution whose moments are a ...
Fabio Deelan Cunden, M. Ligabò, Tommaso Monni   +2 more
semanticscholar   +1 more source

Regularized Limit, Analytic Continuation and Finite-part Integration [PDF]

Analysis and Applications, 2021
. Finite-part integration is a recent method of evaluating a convergent integral in terms of the finite-parts of divergent integrals deliberately in- duced from the convergent integral itself [E. A. Galapon, Proc. R. Soc., A 473, 20160567 (2017)].
E. Galapon
semanticscholar   +1 more source

Fourier and Cauchy-Stieltjes transforms of power laws including stable distributions [PDF]

, 2011
We introduce a class of probability measures whose densities near infinity are mixtures of Pareto distributions. This class can be characterized by the Fourier transform which has a power series expansion including real powers, not only integer powers ...
Takahiro Hasebe
semanticscholar   +1 more source

Exact solution of Chern-Simons-matter matrix models with characteristic/orthogonal polynomials [PDF]

Journal of High Energy Physics, 2016
A bstractWe solve for finite N the matrix model of supersymmetric U(N ) Chern-Simons theory coupled to Nf fundamental and Nf anti-fundamental chiral multiplets of R-charge 1/2 and of mass m, by identifying it with an average of inverse characteristic ...
M. Tierz
semanticscholar   +2 more sources

Some Geometric Properties of the Subordination Function Associated to an Operator-Valued Free Convolution Semigroup [PDF]

Complex Analysis and Operator Theory, 2015
In his article On the free convolution with a semicircular distribution, Biane found very useful characterizations of the boundary values of the imaginary part of the Cauchy–Stieltjes transform of the free additive convolution of a probability measure on
S. Belinschi
semanticscholar   +2 more sources

Averages for Multivariate Random Vectors with Random Weights

Revstat Statistical Journal, 2020
We consider a random weights average of n independent continuous random vectors X1, ..., Xn, where random weights are cuts of [0, 1] by an increasing sequence of the order statistics of a random sample from a uniform [0, 1].
A.R. Soltani , Rasool Roozegar
doaj   +1 more source