Bivariate Uniqueness and Endogeny for the Logistic Recursive Distributional Equation

Abstract

In this article we prove the bivariate uniqueness property for a particular ``max-type'' recursive distributional equation (RDE). Using the general theory developed by Aldous and Bandyopadhyay (2005) we then show that the corresponding recursive tree process (RTP) has no external randomness, more preciously, the RTP is endogenous. The RDE we consider is so called the Logistic RDE, which appears in Aldous' (2001) proof of the $ζ(2)$-limit of the random assignment problem using the local weak convergence method. Thus this work provides a non-trivial application of the general theory developed by Aldous and Bandyopadhyay (2005).