Publications Mathématiques de l'Institut des Hautes Études Scientifiques

, Volume 98, Issue 1, pp 167–212

Determinantal probability measures


DOI: 10.1007/s10240-003-0016-0

Cite this article as:
Lyons, R. Publ. Math. (2003) 98: 167. doi:10.1007/s10240-003-0016-0


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.

Copyright information

© Institut des Hautes Études Scientifiques and Springer-Verlag 2003

Authors and Affiliations

  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA
  2. 2.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA