刊物主题:Mathematics Probability Theory and Stochastic Processes Dynamical Systems and Ergodic Theory Mathematical Biology Partial Differential Equations Functional Analysis Abstract Harmonic Analysis Group Theory and Generalizations
出版者:Springer Berlin / Heidelberg
ISSN:1617-9692
文摘
We point out a simple argument relying on hypercontractivity to describe tail inequalities on the distribution of the largest eigenvalues of random matrices at the rate given by the Tracy–Widom distribution. The result is illustrated on the known examples of the Gaussian and Laguerre unitary ensembles. The argument may be applied to describe the generic tail behavior of eigenfunction measures of hypercontractive operators.