Abstract
We generalize the decomposition method of the finite Markov chains for Poincare inequality in Jerrum et al. (Ann. Appl. Probab., 14, 1741–1765 (2004)) to the reversible continuous-time Markov chains. And inductively, we give the lower bound of spectral gap for the ergodic open Jackson network by the decomposition method and the symmetrization procedure. The upper bound of the spectral gap is also presented.
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