Title: Bivariate Uniqueness in the Logistic Recursive Distributional Equation
Author: Antar Bandyopadhyay
Date: November 2002
Pub: PDF
url: http://www.stat.berkeley.edu/users/antar/629.pdf

Abstract:
In this work we prove the \emph{bivariate uniqueness} property of the
Logistic fixed-point equation, which arise in the study of the 
\emph{random assignment problem}, as discussed by Aldous (2001). 
Using this and the general framework of Aldous and Bandyopadhyay
(2002), we then conclude that the associated 
\emph{recursive tree process} is \emph{endogenous}, and hence the
Logistic variables defined in Aldous' 2001 paper are measurable
with respect to the $\sigma$-field generated by the edge weights. The
method involves construction of an explicit recursion to show the
uniqueness of the associated integral equation.