Results 11 to 20 of about 4,039 (94)

Average Characteristic Polynomials of Determinantal Point Processes [PDF]

, 2015
We investigate the average characteristic polynomial $\mathbb E\big[\prod_{i=1}^N(z-x_i)\big] $ where the $x_i$'s are real random variables which form a determinantal point process associated to a bounded projection operator.
Hardy, Adrien
core   +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   +1 more source

Studies on the Marchenko–Pastur Law

Mathematics
In 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, Ohud A. Alqasem, Maysaa Elmahi Abd Elwahab, Raouf Fakhfakh   +3 more
doaj   +1 more source

Free Probability based Capacity Calculation of Multiantenna Gaussian Fading Channels with Cochannel Interference [PDF]

, 2011
During the last decade, it has been well understood that communication over multiple antennas can increase linearly the multiplexing capacity gain and provide large spectral efficiency improvements.
Bai, Bai, Björn Ottersten, Blum, Chatzinotas, Chatzinotas, Chatzinotas, Choi, Dai, Foschini, Hachem, Hiai, Hiai, Lozano, Martin, Marčenko, Moustakas, Moustakas, Ong, Peacock, Somekh, Somekh, Symeon Chatzinotas, Tempo, Tulino, Voiculescu, Wyner   +26 more
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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   +1 more source

The empirical distribution of the eigenvalues of a Gram matrix with a given variance profile [PDF]

, 2005
Consider a $N\times n$ random matrix $Y_n=(Y_{ij}^{n})$ where the entries are given by $Y_{ij}^{n}=\frac{\sigma(i/N,j/n)}{\sqrt{n}} X_{ij}^{n}$, the $X_{ij}^{n}$ being centered i.i.d. and $\sigma:[0,1]^2 \to (0,\infty)$ being a continuous function called
Hachem, W., Loubaton, P., Najim, J.
core   +5 more sources

Some Results on the Free Poisson Distribution

Axioms
Let 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, Ohud A. Alqasem, Maysaa Elmahi Abd Elwahab, Raouf Fakhfakh   +3 more
doaj   +1 more source

On the ubiquity of the Cauchy distribution in spectral problems

, 2014
We consider the distribution of the values at real points of random functions which belong to the Herglotz-Pick (HP) class of analytic mappings of the upper half plane into itself.
Aizenman, Michael, Warzel, Simone
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Random matrices: Universality of local eigenvalue statistics up to the edge [PDF]

, 2010
This is a continuation of our earlier paper on the universality of the eigenvalues of Wigner random matrices. The main new results of this paper are an extension of the results in that paper from the bulk of the spectrum up to the edge. In particular, we
A. Ruzmaikina, A. Soshnikov, A. Soshnikov, C. Tracy, C. Tracy, K. Johansson, L. Erdős, L. Erdős, M.L. Mehta, P. Forrester, S. Péché, S. Péché, Terence Tao, Van Vu, Y. Sinai, Y. Sinai, Z.D. Bai, Z.D. Bai   +17 more
core   +4 more sources

On $\mathbb{T}$-Transformation of Probability Measures

Mathematics
The 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, Ohud A. Alqasem, Raouf Fakhfakh   +2 more
doaj   +1 more source