Concentration of Lipschitz Functionals of Determinantal and Other Strong Rayleigh Measures

Fast Sampling for Strongly Rayleigh Measures with Application to Determinantal Point Processes

In this note we consider sampling from (non-homogeneous) strongly Rayleigh probability measures. As an important corollary, we obtain a fast mixing Markov Chain sampler for Determinantal Point Processes.

Negative Dependence and the Geometry of Polynomials

We introduce the class of strongly Rayleigh probability measures by means of geometric properties of their generating polynomials that amount to the stability of the latter. This class contains e.g. product measures, uniform random spanning tree measures, and large classes of determinantal probability measures and distributions for symmetric exclusion processes. We show that strongly Rayleigh m...

Multivariate CLT follows from strong Rayleigh property

Let (X1, . . . , Xd) be a random nonnegative integer vector. Many conditions are known to imply a central limit theorem for a sequence of such random vectors, for example, independence and convergence of the normalized covariances, or various combinatorial conditions allowing the application of Stein’s method, couplings, etc. Here, we prove a central limit theorem directly from hypotheses on th...

A Representation for Characteristic Functionals of Stable Random Measures with Values in Sazonov Spaces

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 the strongest form of negative dependence properties. We show that the “natural” Monte Carlo Markov Chain (MCMC) algorithm mixes rapidly in the support of a homogeneous strongly Rayleigh distribution. As a byproduct, our proof implies Markov chains can be used to effici...