2011/03/29 by Igor Artemenko, Artemenko, Igor
Computer Science · Mathematics · #05C99 #Combinatorics (math.CO) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Topological and Geometric Data Analysis #math.CO #msc:05C99
paper · pdf · doi:10.48550/arxiv.1103.5517
This is a Fall 2010 Honours research project done under the supervision of Dr. Vladimir Pestov at the University of Ottawa; 33 pages, 5 figures, uses tkz-graph.sty
arxiv created 2011/03/29 · openalex publication_date 2011/03/29 · arxiv updated 2011/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The law of a finite graph is a probability measure induced by the orbits of the graph under its automorphism group. Every law satisfies the intrinsic mass transport principle, which is also known as unimodularity. We discuss the convergence of sequences of laws of finite graphs. Of particular importance is a conjecture proposed by Aldous and Lyons that claims every unimodular measure is a limit of a sequence of laws. Aside from this open problem, other directions of research are also mentioned. We work out in detail a number of results and examples, some of which are new, and others that have been previously stated without proofs. These results include a new characterization of laws of finite connected graphs, a description of the topological space of paths, and a proof that the compact space of weak limits of laws is convex.