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2015

Universality for Random Matrix Flows with Time-dependent Density

Erdos, Laszlo, Schnelli, Kevin

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We show that the Dyson Brownian Motion exhibits local universality after a very short time assuming that local rigidity and level repulsion hold.

These conditions are verified, hence bulk spectral universality is proven, for a large class of Wigner-like matrices, including deformed Wigner ensembles and ensembles with non-stochastic variance matrices whose limiting densities differ from the Wigner semicircle law.

Universality for Random Matrix Flows with Time-dependent Density · Around

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1955
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Dyson, F.J.:
1962
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Pastur, L.:
1972
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Bakry, D., Émery, M.:
1985
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Voiculescu, D.:
1986
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Mehta, M.L.:
1991
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Yau, H.-T.:
1991
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Fokas, A. S., Its, A. R., Kitaev, A. V.:
1992
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Maassen, H.:
1992
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Voiculescu, D., Dykema, K. J., Nica, A.:
1992
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Boutet de Monvel, A., Pastur, L. and Shcherbina, M.:
1995
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Nica, A., Speicher, R.:
1996
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Pandey, J. N.:
1996
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Biane, P.:
1997
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Pastur, L., Shcherbina, M.:
1997
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Deift, P.:
1999
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