The simple random walk and max-degree walk on a directed graph

Details The simple random walk and max-degree walk on a directed graph The simple random walk and max-degree walk on a directed graph

2006-09-11

arxiv.org/abs/math/0609303v1

Random Structures and Algorithms, vol 34:3, pp. 395-407, 2009.

Mathematics

Combinatorics

Scientific paper

10.1002/rsa.20227

We show bounds on total variation and $L^{\infty}$ mixing times, spectral gap and magnitudes of the complex valued eigenvalues of a general (non-reversible non-lazy) Markov chain with a minor expansion property. This leads to the first known bounds for the non-lazy simple and max-degree walks on a (directed) graph, and even in the lazy case they are the first bounds of the optimal order. In particular, it is found that within a factor of two or four, the worst case of each of these mixing time and eigenvalue quantities is a walk on a cycle with clockwise drift.

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