Determinantal Probability Measures
نویسنده
چکیده
Determinantal point processes have arisen in diverse settings in recent years and have been investigated intensively. We initiate a detailed study of the discrete analogue, the most prominent example of which has been the uniform spanning tree measure. 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.
منابع مشابه
Determinantal probability Basic properties and conjectures
We describe the fundamental constructions and properties of determinantal probability measures and point processes, giving streamlined proofs. We illustrate these with some important examples. We pose several general questions and conjectures. Mathematics Subject Classification (2010). Primary 60K99, 60G55; Secondary 42C30, 37A15, 37A35, 37A50, 68U99.
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