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Let X1, . . . ,Xk and Y 1, . . . , Y m be jointly independent copies of random variables X and Y , respectively. For a fixed total number n of random variables, we aim at maximising M(k,m) := Emax{X1, . . . ,Xk, Y 1, . . . , Y m} in k = n − m ≥ 0, which corresponds to maximising the expected lifetime of an n-component parallel system whose components can be… (More)

Markov-chain Monte Carlo (MCMC) simulation is one of the most versatile and widely-used tools applied in statistical physics. In order for MCMC algorithms to be useful however, it is crucial that they converge rapidly to stationarity. A major breakthrough in the development of efficient MCMC algorithms for statistical-mechanical spin models was the… (More)

- Daniel Tokarev
- 2008

The mean time to extinction of a critical Galton–Watson process with initial population size k is shown to be asymptotically equivalent to two integral transforms: one involving the kth iterate of the probability generating function and one involving the generating function itself. Relating the growth of these transforms to the regular variation of their… (More)

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