scholarly journals A note on computing the distribution of the norm of Hilbert space valued Gaussian random variables

1980 ◽  
Vol 10 (1) ◽  
pp. 19-25 ◽  
Author(s):  
Georg Neuhaus
Keyword(s):  
Hilbert Space ◽  
Random Variables ◽  
Gaussian Random Variables

THE NON-COMMUTATIVE KHINTCHINE INEQUALITIES FOR

2015 ◽  
Vol 16 (5) ◽  
pp. 1103-1123 ◽  
Author(s):  
Gilles Pisier ◽  
Éric Ricard
Keyword(s):  
Hilbert Space ◽  
Von Neumann Algebras ◽  
Free Probability ◽  
Random Variables ◽  
Gaussian Random Variables ◽  
Von Neumann ◽  
Rademacher Functions ◽  
General Sequences ◽  
Mazur Maps ◽  
New Inequalities

We give a proof of the Khintchine inequalities in non-commutative $L_{p}$-spaces for all $0<p<1$. These new inequalities are valid for the Rademacher functions or Gaussian random variables, but also for more general sequences, for example, for the analogues of such random variables in free probability. We also prove a factorization for operators from a Hilbert space to a non-commutative $L_{p}$-space, which is new for $0<p<1$. We end by showing that Mazur maps are Hölder on semifinite von Neumann algebras.

BESSIS–MOUSSA–VILLANI CONJECTURE AND GENERALIZED GAUSSIAN RANDOM VARIABLES

2008 ◽  
Vol 11 (03) ◽  
pp. 313-321 ◽  
Author(s):  
MAREK BOŻEJKO
Keyword(s):  
Hilbert Space ◽  
Real Line ◽  
Real Hilbert Space ◽  
Random Variables ◽  
Positive Definite Function ◽  
Positive Definite ◽  
Definite Function ◽  
Gaussian Random Variables ◽  
The Real ◽  
Bmv Conjecture

In this paper we give the solution of Bessis–Moussa–Villani (BMV) conjecture for the generalized Gaussian random variables [Formula: see text] where f is in the real Hilbert space [Formula: see text]. The main examples of generalized Gaussian random variables are q-Gaussian random variables, (-1 ≤ q ≤ 1), related to q-CCR relation and other commutation relations. We will prove that BMV conjecture is true for all operators A = G(f), B = G(g); i.e. we will show that the function [Formula: see text] is positive-definite function on the real line. The case q = 0, i.e. when G(f) are the free Gaussian (Wigner) random variables and the operators A and B are free with respect to the vacuum trace was proved by Fannes and Petz.23

scholarly journals Performance Degradation in Cross-Eye Jamming Due to Amplitude/Phase Instability between Jammer Antennas

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5027
Author(s):  
Je-An Kim ◽  
Joon-Ho Lee
Keyword(s):  
Performance Analysis ◽  
Phase Difference ◽  
Taylor Expansion ◽  
Amplitude Ratio ◽  
Random Variables ◽  
Performance Degradation ◽  
Analytical Performance ◽  
Phase Instability ◽  
Gaussian Random Variables ◽  
First Order

Cross-eye gain in cross-eye jamming systems is highly dependent on amplitude ratio and the phase difference between jammer antennas. It is well known that cross-eye jamming is most effective for the amplitude ratio of unity and phase difference of 180 degrees. It is assumed that the instabilities in the amplitude ratio and phase difference can be modeled as zero-mean Gaussian random variables. In this paper, we not only quantitatively analyze the effect of amplitude ratio instability and phase difference instability on performance degradation in terms of reduction in cross-eye gain but also proceed with analytical performance analysis based on the first order and second-order Taylor expansion.

scholarly journals Real Zeros of a Class of Hyperbolic Polynomials with Random Coefficients

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Mina Ketan Mahanti ◽  
Amandeep Singh ◽  
Lokanath Sahoo
Keyword(s):  
Random Variables ◽  
Random Coefficients ◽  
Expected Number ◽  
Hyperbolic Polynomial ◽  
Gaussian Random Variables ◽  
Hyperbolic Polynomials ◽  
Asymptotic Value ◽  
Real Zeros ◽  
Number Of Real Zeros

We have proved here that the expected number of real zeros of a random hyperbolic polynomial of the formy=Pnt=n1a1cosh⁡t+n2a2cosh⁡2t+⋯+nnancosh⁡nt, wherea1,…,anis a sequence of standard Gaussian random variables, isn/2+op(1). It is shown that the asymptotic value of expected number of times the polynomial crosses the levely=Kis alson/2as long asKdoes not exceed2neμ(n), whereμ(n)=o(n). The number of oscillations ofPn(t)abouty=Kwill be less thann/2asymptotically only ifK=2neμ(n), whereμ(n)=O(n)orn-1μ(n)→∞. In the former case the number of oscillations continues to be a fraction ofnand decreases with the increase in value ofμ(n). In the latter case, the number of oscillations reduces toop(n)and almost no trace of the curve is expected to be present above the levely=Kifμ(n)/(nlogn)→∞.

Sub-Gaussian random variables

1980 ◽  
Vol 32 (6) ◽  
pp. 483-489 ◽  
Author(s):  
V. V. Buldygin ◽  
Yu. V. Kozachenko
Keyword(s):  
Random Variables ◽  
Gaussian Random Variables
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