Book Review: Probability on graphs: random processes on graphs and lattices

Probability on Graphs Random Processes on Graphs and Lattices

Probability on Graphs Lecture Notes on Stochastic Processes on Graphs and Lattices

Preface Within the menagerie of objects studied in contemporary probability theory, there are a number of related animals that have attracted great interest amongst proba-bilists and physicists in recent years. The overall target of these notes is to identify some of these, and to develop their basic theory. The inspiration for many of these objects comes from physics, but the mathematical subj...

Contact Processes on Random Regular Graphs

We show that the contact process on a random d-regular graph initiated by a single infected vertex obeys the “cutoff phenomenon” in its supercritical phase. In particular, we prove that, when the infection rate is larger than the lower critical value of the contact process on the infinite d-regular tree, there are positive constants C, p depending on the infection rate such that for any ε > 0, ...

The Second King’s Workshop on Random Graphs and Random Processes

Probability on Graphs

The random assignment problem is to minimize the cost of an assignment in a n×n matrix of random costs. In this paper we study this problem for some integer valued cost distributions. We consider both uniform distributions on 1, 2, . . . , m, for m = n or n, and random permutations of 1, 2, . . . , n for each row, or of 1, 2, . . . , n for the whole matrix. We find the limit of the expected cos...