Monte Carlo Markov Chain Algorithms for Sampling Strongly Rayleigh   Distributions and Determinantal Point Processes
  Strongly Rayleigh distributions are natural generalizations of product and determinantal probability distributions and satisfy strongest form of negative dependence properties. We show that the "natural" Monte Carlo Markov Chain (MCMC) is rapidly mixing in the support of a {\em homogeneous} strongly Rayleigh distribution. As a byproduct, our proof implies Markov chains can be used to efficiently generate approximate samples of a $k$-determinantal point process. This answers an open question raised by Deshpande and Rademacher. 
Nima Anari, Shayan Oveis Gharan, Alireza Rezaei
cs.LG cs.DS math.PR