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Conductance and convergence of Markov chains
Abstract: "Let P be an irreducible and strongly aperiodic (i.e. p[subscript ii] [greater than or equal to] 1/2 [for all] i) stochastic matrix. We obtain non-asymptotic bounds for the convergence rate of a Markov chain with transition matrix P in terms of the conductance of P. These results have been so far obtained only for time-reversible Markov chains via partially linear algebraic arguments [Al86][A87][SJ87]. Our proofs eliminate the linear algebra and therefore naturally extend to general Markov chains. The key new idea is to view the action of a strongly aperiodic stochastic matrix as a weighted averaging along the edges of the underlying graph of P. Our results suggest that the conductance (rather than the second largest eigenvalue) best quantifies the rate of convergence of stongly aperiodic Markov chains."
- "Abstract: "Let P be an irreducible and strongly aperiodic (i.e. p[subscript ii] [greater than or equal to] 1/2 [for all] i) stochastic matrix. We obtain non-asymptotic bounds for the convergence rate of a Markov chain with transition matrix P in terms of the conductance of P. These results have been so far obtained only for time-reversible Markov chains via partially linear algebraic arguments [Al86][A87][SJ87]. Our proofs eliminate the linear algebra and therefore naturally extend to general Markov chains. The key new idea is to view the action of a strongly aperiodic stochastic matrix as a weighted averaging along the edges of the underlying graph of P. Our results suggest that the conductance (rather than the second largest eigenvalue) best quantifies the rate of convergence of stongly aperiodic Markov chains.""@en
- "Conductance and convergence of Markov chains"@en
- "Conductance and convergence of Markov chains"