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This paper develops bounds on the rate of decay of powers of Markov kernels
on finite state spaces. These are combined with eigenvalue estimates to give
good bounds on the rate of convergence to sta...
LOGARITHMIC SOBOLEV INEQUALITIES FOR FINITE MARKOV CHAINS
Sobolev inequality MARKOV CHAINS
2015/8/26
This is an expository paper on the use of logarithmic Sobolev inequalities
for bounding rates of convergence of Markov chains on finite state
spaces to their stationary distributions. Logarithmic So...
We introduce geometric comparison inequalities that give bounds on the eigenvalues of a reversible Markov chain in terms of the eigenvalues of a second chain. The bounds are applied to get sharp resul...