Volume 78, Number 1, April 2007
|Number of page(s)||5|
|Published online||12 March 2007|
On the top eigenvalue of heavy-tailed random matrices
Service de Physique Théorique, Orme des Merisiers, CEA Saclay - 91191 Gif-sur-Yvette Cedex, France
2 Science & Finance, Capital Fund Management - 6 Bd Haussmann, 75009 Paris, France
3 Service de Physique de l'État Condensé, Orme des Merisiers, CEA Saclay - 91191 Gif-sur-Yvette Cedex, France
Accepted: 10 February 2007
We study the statistics of the largest eigenvalue of random matrices with IID entries of variance , but with power law tails . When , converges to 2 with Tracy-Widom fluctuations of order , but with large finite N corrections. When , is of order and is governed by Fréchet statistics. The marginal case 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.
PACS: 02.10.Yn – Matrix theory / 02.50.-r – Probability theory, stochastic processes, and statistics / 89.65.Gh – Economics; econophysics, financial markets, business and management
© Europhysics Letters Association, 2007
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