Conductance and the rapid mixing property for Markov chains: the approximation of permanent resolved
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Mixing of random walks and other diffusions on a graph
Surveys in combinatorics, 1995
Sudden emergence of a giant k-core in a random graph
Journal of Combinatorial Theory Series B
Faster mixing via average conductance
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Regular Article: The Diameter of Sparse Random Graphs
Advances in Applied Mathematics
The diameter of sparse random graphs
Random Structures & Algorithms
Random Structures & Algorithms
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In this article we present a study of the mixing time of a random walk on the largest component of a supercritical random graph, also known as the giant component. We identify local obstructions that slow down the random walk, when the average degree d is at most O($ \sqrt{\ln n} $), proving that the mixing time in this case is Θ((n-d)2) asymptotically almost surely. As the average degree grows these become negligible and it is the diameter of the largest component that takes over, yielding mixing time Θ(n-d) a.a.s.. We proved these results during the 2003–04 academic year. Similar results but for constant d were later proved independently by Benjamini et al. in [3]. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008 Most of this work was completed while the author was a research fellow at the School of Computer Science, McGill University.