Regularity of Self-Diffusion Coefficient
We consider the infinite particle system in Z d known commonly as symmetric random walk with simple exclusion. This consists of particles in Z d , each trying to execute a more or less independent random walk with jump probabilities p(x). We assume that p(x) is symmetric, i.e., p(x) = p(−x), and that it has finite range. If d = 1, we assume, in addition, that p(1) +p(−1) < 1, so that only the one-dimensional nearest neighbor random walk is excluded. Particles wait for an exponential time, pick a random jump size x with probability p(x), and try to jump to a new site defined by a jump equal to x. If the site is free, the jump is completed and things start all over again. Otherwise the jump is disallowed and things start all over again with the particle remaining in the old site. All the particles are doing this simultaneously and independently of each other. See  for a discussion of the model.
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