1208.2691 (Johannes Bausch)

On the Efficient Calculation of a Linear Combination of Chi-Square
Random Variables with an Application in Counting String Vacua    [PDF]

Johannes Bausch

As a first result, an explicit analytic expression for the density of the sum of two Gamma random variables is derived. Then a computationally efficient algorithm to numerically calculate the linear combination of an even number of chi^2_r random variables is developed. An explicit expression for the error bound is obtained. As an application, the exponential dependence of the eigenvalue fluctuation probability of a random matrix model for 4d supergravity with N scalar fields is found to be of the asymptotic form exp(-0.35N).

View original: http://arxiv.org/abs/1208.2691