Endogeny for the Logistic Recursive Distributional Equation

Abstract : In this article we prove the endogeny and bivariate uniqueness property for a particular "max-type" recursive distributional equation (RDE). The RDE we consider is so called the Logistic RDE, which appears in the proof of the ζ(2)-limit of the random assignment problem using the local weak convergence method (Aldous 2001). This article provides a non-trivial application of the general theory developed in (Bandyopadhyay and Aldous 2005). The proofs involves analytic arguments, which illustrate the need to develop more analytic tools for studying such max-type RDEs.