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Universality of the Edge Distribution of Eigenvalues of Wigner Random Matrices with Polynomially Decaying Distributions of Entries

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Abstract

We consider an ensemble of Wigner symmetric random matrices A n ={a ij }, i,j=1, . . . ,n with matrix elements a ij , being i.i.d. symmetrically distributed random variables We assume that and that

for p>18. We prove that the distribution of the k (k=1,2, . . . ) largest (smallest) eigenvalues has a universal limit as n→∞ (the Tracy-Widom distribution).

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  1. Departments of Statistics and Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    A. Ruzmaikina

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Communicated by P. Sarnak

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Ruzmaikina, A. Universality of the Edge Distribution of Eigenvalues of Wigner Random Matrices with Polynomially Decaying Distributions of Entries. Commun. Math. Phys. 261, 277–296 (2006). https://doi.org/10.1007/s00220-005-1386-6

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