Leonid A. Pastur

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We study the normalized trace gn(z) = n −1tr (H−zI)−1 of the resolvent of n×n real symmetric matrices H = [(1+ δjk)Wjk/ √ n]nj,k=1 assuming that their entries are independent but not necessarily identically distributed random variables. We develop a rigorous method of asymptotic analysis of moments of gn(z) for |Iz| ≥ η0 where η0 is determined by the second(More)
We develop direct and inverse scattering theory for Jacobi operators with steplike coefficients which are asymptotically close to different finite-gap quasi-periodic coefficients on different sides. We give a complete characterization of the scattering data, which allow unique solvability of the inverse scattering problem in the class of perturbations with(More)
The paper deals with the eigenvalue statistics of n n random Hermitian matrices as n ! 1. We consider a certain class of unitary invariant matrix probability distributions which have been actively studied in recent years in the quantum eld theory (QFT). These ensembles are natural extensions of the archetype Gaussian ensemble well known and widely studied(More)
We study Bose-Einstein Condensation (BEC) in the Infinite-Range Hopping BoseHubbard model for repulsive on-site particle interaction in presence of ergodic random one-site potentials with different distributions. We show that the model is exactly soluble even if the on-site interaction is random. But in contrast to the non-random case [BD], we observe here(More)
From the standpoint of Information theory, a time and frequency selective Ricean ergodic MIMO channel can be represented in the Hilbert space l<sup>2</sup>(&#x2124;) by a random ergodic self-adjoint operator whose Integrated Density of States (IDS) governs the behavior of the Shannon's mutual information. In this paper, it is shown that when the numbers of(More)
the X ij being centered, independent and identically distributed random variables with unit variance and (σij (n);1 ≤ i ≤N,1 ≤ j ≤ n) being an array of numbers we shall refer to as a variance profile. In this article, we study the fluctuations of the random variable log det(YnY ∗ n + ρIN ), where Y ∗ is the Hermitian adjoint of Y and ρ > 0 is an additional(More)
The paper deals with the eigenvalue statistics of n n random Hermitian matrices as n!1. We consider a certain class of unitary invariant matrix probability distributions which have been actively studied in recent years in the quantum eld theory (QFT). These ensembles are natural extensions of the archetype Gaussian ensemble well known and widely studied in(More)
We study Bose-Einstein Condensation (BEC) in the Infinite-Range Hopping Bose-Hubbard model for repulsive on-site particle interaction in presence of ergodic random one-site potentials with different distributions. We show that the model is exactly soluble even if the on-site interaction is random. But in contrast to the non-random case [BD], we observe here(More)
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