Determinantal probability measures

Details Determinantal probability measures Determinantal probability measures

2002-04-26

arxiv.org/abs/math/0204325v4

Publ. Math. Inst. Haute\'Etudes Sci. 98 (2003), 167-212.

Mathematics

Probability

50 pp; added reference to revision. Revised introduction and made other small changes

Scientific paper

Determinantal point processes have arisen in diverse settings in recent years and have been investigated intensively. We study basic combinatorial and probabilistic aspects in the discrete case. Our main results concern relationships with matroids, stochastic domination, negative association, completeness for infinite matroids, tail triviality, and a method for extension of results from orthogonal projections to positive contractions. We also present several new avenues for further investigation, involving Hilbert spaces, combinatorics, homology, and group representations, among other areas.

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