21 research outputs found
The simple random walk and max-degree walk on a directed graph
We show bounds on total variation and 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