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We show global uniqueness of the solution to a class of constrained variational problems, using scaling properties. This is used to establish the essential uniqueness of solutions of a large deviations problem in multiple dimensions. The result is motivated by models of buffers, and in particular the probability of, and typical path to overflow in the limit of small buffers, which we analyze.

A new parallel algorithm for simulating Ising spin systems is presented. The sequential prototype is the n-fold way algorithm cite{BKL75}, which is efficient but is hard to parallelize using conservative methods. Our parallel algorithm is optimistic. Unlike other optimistic algorithms, e.g., Time Warp, our algorithm is synchronous. It also belongs to the class of simulations known as ``relaxation'' cite{CS8 hence it is named ``synchronous relaxation.'' We derive performance guarantees for this algorithm. If N is the number of PEs, then under weak assumptions we show that the number of correct events processed per unit of time is, on average, at least of order N/log(N). All communication delays, processing time, and busy waits are taken into account., Comment: Extended abstract. Conference version. The full paper in preparation