Title: A characterization of the Kummer distributions on symmetric matrices
Authors: Pierre Vallois - Université de Lorraine (France) [presenting]
Abstract: A characterization of the Kummer distributions of type $2$ says that if $X,Y_1$ and $Y_2$ are independent random variables such that $Y_1$ and $Y_2$ are gamma distributed, with suitable parameters, then $L(X)=L(Y_1/(1+Y_2/(1+X)))$ if, and only if $X$ has the Kummer distribution. The aim is to extend this characterization to the case where $X,Y_1$ and $Y_2$ are valued in the cone of symmetric, positive definite real matrices. For the proof, we study the convergence of continued fractions with random matrices entries.