Most chance difficulties contain random variables listed through area and/or time. These difficulties virtually always have  a model within which house and/or time are taken to be discrete. This quantity bargains with parts during which the discrete model is extra usual than the continual one, maybe even the single one than may be formulated with out advanced structures and equipment.
The five papers of this quantity talk about difficulties during which there was major development within the previous couple of years; they're inspired by way of, or were built in parallel with, statistical physics. They comprise questions on asymptotic form for stochastic development types and for random clusters; life, position and houses of part transitions; velocity of convergence to equilibrium in Markov chains, and particularly for Markov chains in response to versions with a section transition; cut-off phenomena for random walks.
The articles may be learn independently of one another. Their unifying subject matter is that of types outfitted on discrete areas or graphs. Such versions are usually effortless to formulate. Correspondingly, the publication calls for relatively little past wisdom of the equipment of probability.

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