Extremal spacings of random unitary matrices

Details Extremal spacings of random unitary matrices Extremal spacings of random unitary matrices

2012-04-13

arxiv.org/abs/1204.3023v2

Physics

Mathematical Physics

Scientific paper

Extremal spacings between unimodular eigenvalues of random unitary matrices of size N pertaining to circular ensembles are investigated. Probability distributions for the minimal spacing for various ensembles are derived for N=4. We show that for large matrices the average minimal spacing s_min of a random unitary matrix behaves as N^(-1/(1+B)) for B equal to 0,1 and 2 for circular Poisson, orthogonal and unitary ensembles, respectively. For these ensembles also asymptotic probability distributions P(s_min) are obtained and the statistics of the largest spacing s_max are investigated.

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