 
Summary: Edge Flows in the Complete
RandomLengths Network*
David J. Aldous,1
Shankar Bhamidi2
1
Department of Statistics, University of California, Berkeley, California 947203860;
email: aldous@stat.berkeley.edu
2
Department of Statistics, University of North Carolina, Chapel Hill, North Carolina
27599; email: hamidi@email.unc.edu
Received 30 July 2007; accepted 28 November 2008; received in final form 18 February 2009
Published online 28 January 2010 in Wiley Online Library (wileyonlinelibrary.com).
DOI 10.1002/rsa.20306
ABSTRACT: Consider the complete nvertex graph whose edgelengths are independent exponen
tially distributed random variables. Simultaneously for each pair of vertices, put a constant flow
between them along the shortest path. Each edge gets some random total flow. In the n limit
we find explicitly the empirical distribution of these edgeflows, suitably normalized. © 2010 Wiley
Periodicals, Inc. Random Struct. Alg., 37, 271311, 2010
Keywords: flow; percolation tree; random graph; random network
1. INTRODUCTION
