Séminaire Calcul Formel

Differential equations for the expectation of the Euler characteristic of random manifolds

by Prof. Nobuki Takayama (Kobe University)




We give an approximate formula for the distribution of the largest eigenvalue of real Wishart matrices by the expected Euler characteristic method for general dimension. The formula is expressed in terms of a definite integral with parameters. We derive a differential equation satisfied by the integral for the 2×2 matrix case and perform a numerical analysis of it.