منابع مشابه
Diffusion at the random matrix hard edge
We show that the limiting minimal eigenvalue distributions for a natural generalization of Gaussian sample-covariance structures (the “beta ensembles”) are described by the spectrum of a random diffusion generator. By a Riccati transformation, we obtain a second diffusion description of the limiting eigenvalues in terms of hitting laws. This picture pertains to the so-called hard edge of random...
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Inter-relations between random matrix ensembles with different symmetry types provide inter-relations between generating functions for the gap probabilites at the spectrum edge. Combining these in the scaled limit with the exact evaluation of the gap probabilities for certain superimposed ensembles with orthogonal symmetry allows for the exact evaluation of the gap probabilities at the hard and...
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Let Λ be the limiting smallest eigenvalue in the general (β, a)-Laguerre ensemble of random matrix theory. That is, Λ is the n ↑ ∞ distributional limit of the (scaled) minimal point drawn from the density proportional to ∏ 1≤i 0, a > −1; for β = 1, 2, 4 and integer a, this object governs the singular values of certain rank n Ga...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2016
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-016-0733-1