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Summary We establish large deviation principles for the stationary and the individual empirical fields of Poisson, and certain interacting, random fields of marked point particles in Rd. The underlying topologies are induced by a class of not necessarily bounded local functions, and thus finer than the usual weak topologies. Our methods yield further that the limiting behaviour of conditional Poisson distributions, as well as certain distributions of Gibbsian type, is governed by the maximum entropy principle. We also discuss various applications and examples.

Large deviations and the maximum entropy principle for marked point random fields