7 citations · 7 across the 5 of their papers we have counts for
4 papers · 1 filter
Sharp edge, vertex, and mixed Cheeger type inequalities for finite Markov kernels
Ravi Montenegro
We show how the evolving set methodology of Morris and Peres can be used to show Cheeger inequalities for bounding the spectral gap of a finite Markov kernel. This leads to sharp v…
Eigenvalues of non-reversible Markov chains: their connection to mixing times
Ravi Montenegro
This paper originally showed a lower bound on mixing time for a non-reversible Markov chain in terms of its largest non-trivial eigenvalue, and used this to re-derive some generali…
Mixing Time Bounds via the Spectral Profile
Sharad Goel, Ravi Montenegro, Prasad Tetali
On complete, non-compact manifolds and infinite graphs, Faber-Krahn inequalities have been used to estimate the rate of decay of the heat kernel. We develop this technique in the s…
Vertex and edge expansion properties for rapid mixing
Ravi Montenegro
We show a strict hierarchy among various edge and vertex expansion properties of Markov chains. This gives easy proofs of a range of bounds, both classical and new, on chi-square d…