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} in k = n − m ≥ 0, which corresponds to maximising the expected lifetime of an n-component parallel system whose components can be chosen from two different types. We show that the lattice {M (k, m): k, m ≥ 0} is concave, give sufficient conditions on X and Y for M (n, 0) to be always or ultimately maximal and derive a bound on the number of sign changes… (More)

We prove rapid mixing of the Prokofiev-Svistunov (or worm) algorithm for the zero-field ferro-magnetic Ising model, on all finite graphs and at all temperatures. As a corollary, we show how to rigorously construct simple and efficient approximation schemes for the Ising susceptibility and two-point correlation function. Markov-chain Monte Carlo (MCMC)… (More)

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