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Point processes with specified correlation functions

Tuesday 13th June 2006 - 14:15 to 15:15
INI Seminar Room 1

Given a point process, in Euclidean space or on a lattice, the corresponding k-point correlation function, for k=1,2, . . ., expresses the probability of finding particles at k specified points. Here we ask a converse question: if we are given a finite number of candidate correlation functions, say those for k=1,2, . . . , n, does there exist a point process which realizes these correlations? We give some partial answers to this question and discuss some examples.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons