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تسجيل مستخدم جديدHydrodynamical spectral evolution for random matrices
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The eigenvalues of the matrix structure $X + X^{(0)}$, where $X$ is a random Gaussian Hermitian matrix and $X^{(0)}$ is non-random or random independent of $X$, are closely related to Dyson Brownian motion. Previous works have shown how an infinite hierarchy of equations satisfied by the dynamical correlations become triangular in the infinite density limit, and give rise to the complex Burgers equation for the Greens function of the corresponding one-point density function. We show how this and analogous partial differential equations, for chiral, circular and Jaco
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This is an elementary review, aimed at non-specialists, of results that have been obtained for the limiting distribution of eigenvalues and for the operator norms of real symmetric random matrices via the method of moments. This method goes back to a
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The celebrated elliptic law describes the distribution of eigenvalues of random matrices with correlations between off-diagonal pairs of elements, having applications to a wide range of physical and biological systems. Here, we investigate the genera
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Motivated by the long-time transport properties of quantum waves in weakly disordered media, the present work puts random Schrodinger operators into a new spectral perspective. Based on a stationary random version of a Floquet type fibration, we redu
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We generally study the density of eigenvalues in unitary ensembles of random matrices from the recurrence coefficients with regularly varying conditions for the orthogonal polynomials. First we calculate directly the moments of the density. Then, by
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We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition prin
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