Matzinger (Random Structure Algorithm 15 (1999a) 196) showed how to reconstruct almost every three color scenery, that is a coloring of the integers with three colors, by observing it along the path of a simple random walk, if this scenery is the outcome of an i.i.d. process. This reconstruction...

The so-called swapping algorithm was designed to simulate from spin glass distributions, among others. In this note we show that it mixes rapidly, in a very simple disordered system, the Hopfield model with two patterns.

We analyze the simulated annealing algorithm with an energy function Ut that depends on time. Assuming some regularity conditions on Ut (especially that Ut does not change too quickly in time), and choosing a logarithmic cooling schedule for the algorithm, we derive bounds on the Radon-Nikodym...

We show that for sufficiently large knapsacks the associated Markov chain on the state space of the admissible packings of the knapsack is rapidly mixing. Our condition basically states that at least half of all items should fit into the knapsack. This is much weaker than the condition assumed...