Year: 2007
Type: article
Abstract: We study the statistics of the largest eigenvalue λ max of N × N random matrices with IID entries of variance 1/ N , but with power law tails P ( M ij ) ∼ | M ij | −1−μ . When μ > 4, λ max converges to 2 with Tracy-Widom fluctuations of order N −2/3 , but with large finite N corrections. When μ < 4, λ max is of order N 2/μ−1/2 and is governed by Fréchet statistics. The marginal case μ = 4 provides a new class of limiting distribution that we compute explicitly. We extend these results to sample covariance matrices, and show that extreme events may cause the largest eigenvalue to significantly exceed the Marčenko-Pastur edge.
Source: Europhysics Letters (EPL)
Authors: G Biroli, J.-P Bouchaud, M Potters
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2008732718