The smallest eigenvalue distribution in the real Wishart-Laguerre ensemble with even topology

Abstract

We consider rectangular random matrices of size p × n belonging to the real WishartLaguerre ensemble also known as the chiral Gaussian orthogonal ensemble. This ensemble appears in many applications like QCD, mesoscopic physics, and time series analysis. We are particularly interested in the distribution of the smallest non-zero eigenvalue and the gap probability to find no eigenvalue in an interval [0, t]. While for odd topology ν = n -p explicit closed results are known for finite and infinite matrix size, for even ν > 2 only recursive expressions in p are available. The smallest eigenvalue distribution as well as the gap probability for general even ν is equivalent to expectation values o..