Random matrices and the average topology of the intersection of two quadrics
Algebraic Topology
2013-06-19 v3 Algebraic Geometry
Probability
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.
Keywords
Cite
@article{arxiv.1205.2089,
title = {Random matrices and the average topology of the intersection of two quadrics},
author = {Antonio Lerario},
journal= {arXiv preprint arXiv:1205.2089},
year = {2013}
}