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- Wlodzimierz Bryc
- SIAM Review
- 1996

- Reza Rashidi Far, Tamer Oraby, Wlodzimierz Bryc, Roland Speicher
- IEEE Transactions on Information Theory
- 2008

In a frequency-selective slow-fading channel in a multiple-input multiple-output (MIMO) system, the channel matrix is of the form of a block matrix. A method is proposed to calculate the limit of the eigenvalue distribution of block matrices if the size of the blocks tends to infinity. Asymptotic eigenvalue distribution of is also calculated, where the… (More)

- Wlodzimierz Bryc
- 2001

We analyze and identify stationary fields with linear regressions and quadratic conditional variances. We give sufficient conditions to determine one dimensional distributions uniquely as normal, and as certain compactly-supported distributions. Our technique relies on orthogonal polynomials, which under our assumptions turn out to be a version of the so… (More)

- Wlodzimierz Bryc
- Applied Mathematics and Computation
- 2007

This short note explains how to use ready-to-use components of symbolic software to convert between the free cumulants and the moments of measures without sophisticated programming. This allows quick access to low order moments of free convolutions of measures, which can be used to test whether a given probability measure is a free convolution of other… (More)

- Wlodzimierz Bryc
- Applied Mathematics and Computation
- 2002

This paper presents two simple formulas for approximation of the standard normal right tail probabilities, and indicates the method of computing approximations of higher order. One of the approximations relies on two simple numerical constants, has absolute error of 0.00071 and relative error 0.023; the other uses four numerical constants, has absolute… (More)

- Wlodzimierz Bryc
- 2001

We show that classical processes corresponding to operators which satisfy a q-commutative relation have linear regressions and quadratic conditional variances. From this we deduce that Bell’s inequality for their covariances can be extended from q = −1 to the entire range −1 ≤ q < 1. Corrections of Sunday, February 29, 2004 at 15:40 The following… (More)

- Reza Rashidi Far, Tamer Oraby, Wlodzimierz Bryc, Roland Speicher
- ArXiv
- 2006

In a frequency selective slow-fading channel in a MIMO system, the channel matrix is of the form of a block matrix. This paper proposes a method to calculate the limit of the eigenvalue distribution of block matrices if the size of the blocks tends to infinity. While it considers random matrices, it takes an operator-valued free probability approach to… (More)

- Wlodzimierz Bryc
- 2008

In Bryc(1998) we determined one dimensional distributions of a stationary field with linear regressions (1) and quadratic conditional variances (2) under a linear constraint (7) on the coefficients of the quadratic expression (3). In this paper we show that for stationary Markov chains with linear regressions and quadratic conditional variances the… (More)

- WLODZIMIERZ BRYC
- 2000

Motivated by the theory of large deviations, we introduce a class of non-negative non-linear functionals that have a variational “rate function” representation.

- Reza Rashidi Far, Tamer Oraby, Wlodzimierz Bryc, Roland Speicher
- ArXiv
- 2007

In a frequency selective slow-fading channel in a MIMO system, the channel matrix is of the form of a block matrix. We propose a method to calculate the limit of the eigenvalue distribution of block matrices if the size of the blocks tends to infinity. We will also calculate the asymptotic eigenvalue distribution of HH ∗, where the entries of H are jointly… (More)

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