Sharif Digital Repository

Strongly Rayleigh measures are an important class of negatively dependent (repulsive) probability measures. These measures are defined via a geometric condition, called “real stability”, on their generating polynomials, and have interesting probabilistic properties. On one important property of negatively dependent measures is their rigid dependence structure. In other words, the it is impossible for these measures to have strong overall dependencies. In this thesis, we study two manifestations if this phenomenon: (1) paving property and (2) tail triviality. Informally, the paving property states that it is possible to partition the set of the components of every strongly Rayleigh random...