Elementary bounds on Poincaré and log-Sobolev constants for decomposable Markov chains
Elementary bounds on Poincaré and log-Sobolev constants for decomposable Markov chains
We consider finite-state Markov chains that can be naturally decomposed into smaller “projection” and “restriction” chains. Possibly this decomposition will be inductive, in that the restriction chains will be smaller copies of the initial chain. We provide expressions for Poincaré (resp. log-Sobolev) constants of the initial Markov chain in terms …