A novel upper bound is presented for the second largest eigenvalue of a finite reversible time-homogeneous Markov chain as a function of three parameters, namely the smallest transition probability, the underlying structure of the chain, and the skewness of the equilibrium distribution. Simulated annealing (SA) is an example of a probabilistic algorithm that is widely used for solving combinatorial optimization problems, wherein the transition probabilities are controlled by a certain temperature parameter T<0. Using the results presented, it is possible to bound the time constant of convergence of SA to equilibrium at any fixed temperature T<0, and also to study the temperature asymptotics, namely the growth of this bound as T to 0.
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