منابع مشابه
Continuum Percolation for Gaussian zeroes and Ginibre eigenvalues
We study continuum percolation on certain negatively dependent point processes on R. Specifically, we study the Ginibre ensemble and the planar Gaussian zero process, which are the two main natural models of translation invariant point processes on the plane exhibiting local repulsion. For the Ginibre ensemble, we establish the uniqueness of infinite cluster in the supercritical phase. For the ...
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We consider the ensemble of real Ginibre matrices conditioned to have positive fraction α > 0 of real eigenvalues. We demonstrate a large deviations principle for the joint eigenvalue density of such matrices and introduce a two phase log-gas whose stationary distribution coincides with the spectral measure of the ensemble. Using these tools we provide an asymptotic expansion for the probabilit...
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Let Sn be the positive real symmetric matrix of order n with (i, j ) entry equal to ( i + j − 2 j − 1 ) , and let x be a positive real number. Eigenvalues of the Hadamard (or entry wise) power S n are considered. In particular for k a positive integer, it is shown that both the Perron root and the trace of S n are approximately equal to 4 4k−1 ( 2n− 2 n− 1 )k . © 2005 Elsevier Inc. All rights r...
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Let Π be a translation invariant point process on the complex plane C and let D ⊂ C be a bounded open set. We ask what does the point configuration Πout obtained by taking the points of Π outside D tell us about the point configuration Πin of Π inside D? We show that for the Ginibre ensemble, Πout determines the number of points in Πin. For the translation-invariant zero process of a planar Gau...
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Let G be a graph of order n with signless Laplacian eigenvalues q1, . . . , qn and Laplacian eigenvalues μ1, . . . , μn. It is proved that for any real number α with 0 < α 6 1 or 2 6 α < 3, the inequality qα 1 + · · · + qα n > μ1 + · · · + μn holds, and for any real number β with 1 < β < 2, the inequality q 1 + · · ·+ q n 6 μβ1 + · · ·+ μ β n holds. In both inequalities, the equality is attaine...
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2018
ISSN: 1083-6489
DOI: 10.1214/18-ejp234