Let X_R be the zero locus in RP^n of one or two independently and Weyl distributed random real quadratic forms (this is the same as requiring that the corresponding symmetric matrices are in the Gaussian Orthogonal Ensemble). We prove that the sum of the Betti numbers of X_R behaves asymptotically as n (when n goes to infinity). The methods we use combine Random Matrix Theory, Integral geometry and spectral sequences.

Random matrices and the average topology of the intersection of two quadrics

Lerario, Antonio
2015

Abstract

Let X_R be the zero locus in RP^n of one or two independently and Weyl distributed random real quadratic forms (this is the same as requiring that the corresponding symmetric matrices are in the Gaussian Orthogonal Ensemble). We prove that the sum of the Betti numbers of X_R behaves asymptotically as n (when n goes to infinity). The methods we use combine Random Matrix Theory, Integral geometry and spectral sequences.
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https://arxiv.org/abs/1205.2089
Lerario, Antonio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/32533
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