منابع مشابه
Determinantal Random Point Fields
The paper contains an exposition of recent as well as sufficiently old results on determinantal random point fields . We start with some general theorems including the proofs of the necessary and sufficient condition for the existence of determinantal random point field and a criterion for the weak convergence of its the distribution. In the second section we proceed with the examples of the de...
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We prove that, under fairly general conditions, properly rescaled determinantal random point field converges to a generalized Gaussian random process.
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Abstract Tracy and Widom showed that fundamentally important kernels in random matrix theory arise from systems of differential equations with rational coefficients. More generally, this paper considers symmetric Hamiltonian systems and determines the properties of kernels that arise from them. The inverse spectral problem for self-adjoint Hankel operators gives sufficient conditions for a self...
متن کاملGaussian Limit for Determinantal Random Point Fields by Alexander Soshnikov
We prove that, under fairly general conditions, a properly rescaled de-terminantal random point field converges to a generalized Gaussian random process. 1. Introduction and formulation of results. Let E be a locally compact Hausdorff space satisfying the second axiom of countability, B—σ-algebra of Borel subsets and µ a σ-finite measure on (E, B), such that µ(K) < ∞ for any compact K ⊂ E. We d...
متن کاملStatistics of Extreme Spasings in Determinantal Random Point Processes
Determinantal (a.k.a. fermion) random point processes were introduced in probability theory by Macchi about thirty years ago ([13], [14], [3]). In the last ten years the subject has attracted a considerable attention due to its rich connections to Random Matrix Theory, Combinatorics, Representation Theory, Random Growth Models, Number Theory and several other areas of mathematics. We refer the ...
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ژورنال
عنوان ژورنال: Russian Mathematical Surveys
سال: 2000
ISSN: 0036-0279,1468-4829
DOI: 10.1070/rm2000v055n05abeh000321