Gap probabilities in non-Hermitian random matrix theory
نویسندگان
چکیده
منابع مشابه
Gap Probabilities in Non-Hermitian Random Matrix Theory
We compute the gap probability that a circle of radius r around the origin contains exactly k complex eigenvalues. Four different ensembles of random matrices are considered: the Ginibre ensembles and their chiral complex counterparts, with both complex (β = 2) or quaternion real (β = 4) matrix elements. For general non-Gaussian weights we give a Fredholm determinant or Pfaffian representation ...
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Department of Mathematics and Statistics and School of Physics, University of Melbourne, Victoria 3010, Australia Email: [email protected] The probability for the exclusion of eigenvalues from an interval (−x, x) symmetrical about the origin for a scaled ensemble of Hermitian random matrices, where the Fredholm kernel is a type of Bessel kernel with parameter a (a generalisation of the ...
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The gap probabilities at the hard and soft edges of scaled random matrix ensembles with orthogonal symmetry are known in terms of τ -functions. Extending recent work relating to the soft edge, it is shown that these τ -functions, and their generalizations to contain a generating function like parameter, can be expressed as Fredholm determinants. These same Fredholm determinants also occur in ex...
متن کاملGap probabilities for double intervals in hermitian random matrix ensembles as τ-functions - the Bessel kernel case
The probability for the exclusion of eigenvalues from an interval (−x, x) symmetrical about the origin for a scaled ensemble of Her-mitian random matrices, where the Fredholm kernel is a type of Bessel kernel with parameter a (a generalisation of the sine kernel in the bulk scaling case), is considered. It is shown that this probability is the square of a τ-function, in the sense of Okamoto, fo...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2009
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.3133108