2012/08/31 by Johannes Bausch · 1 citation
Mathematics · Physics and Astronomy · #Eigenvalues and eigenvectors #Exponential function #Exponential growth #Expression (computer science) #Independent and identically distributed random variables #Logarithm #Quantum Chromodynamics and Particle Interactions #Random Matrices and Applications #Random variable #Scalar (mathematics) #Square (algebra) #Theoretical and Computational Physics #hep-th #math.PR #msc:15A18 #msc:60G50 #msc:81T30 #msc:83E30 #msc:83E50
paper · pdf · doi:10.1088/1751-8113/46/50/505202
published as J. Phys. A: Math. Theor. 46 (2013) 505202 · 21 pages, 19 figures. 3rd version
openalex publication_date 2013/11/26 · arxiv created 2013/11/27 · arxiv updated 2013/11/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Linear combinations of chi square random variables occur in a wide range of fields. Unfortunately, a closed, analytic expression for the probability density function is not yet known. Starting out from an analytic expression for the density of the sum of two gamma variables, a computationally efficient algorithm to numerically calculate the linear combination of chi square random variables is developed. An explicit expression for the error bound is obtained. The proposed technique is shown to be computationally efficient, i.e. only polynomial in growth in the number of terms compared to the exponential growth of most other methods. It provides a vast improvement in accuracy and shows only logarithmic growth in the required precision. In addition, it is applicable to a much greater number of terms and currently the only way of computing the distribution for hundreds of terms. 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).