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تسجيل مستخدم جديدLarge gaps between random eigenvalues
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We show that in the point process limit of the bulk eigenvalues of $beta$-ensembles of random matrices, the probability of having no eigenvalue in a fixed interval of size $lambda$ is given by [bigl( kappa_{beta}+o(1)bigr)lambda^{gamma_{beta}}expbiggl(-{bet a}{64}lambda^2+biggl({beta}{8}-{1}{4}biggr)lambdabiggr)] as $lambdatoinfty$, where [gamma_{beta}={1}{4}biggl({beta}{2}+{2}{beta}-3biggr)] and $kappa_{beta}$ is an undetermined positive constant. This is a slightly corrected version of a prediction by Dyson [J. Math. Phys. 3 (1962) 157--165]. Our proof uses the new Brownian carousel representation of the limit process, as well as the Cameron--Martin--Girsanov transformation in stochastic calculus.
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