CONTENTS Reference

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Weighted Configuration Model

The configuration model is one of the most successful models for generating uncorrelated random networks. We analyze its behavior when the expected degree sequence follows a power law with exponent smaller than two. In this situation, the resulting network can be viewed as a weighted network with non trivial correlations between strength and degree. Our results are tested against large scale numerical simulations, finding excellent agreement.Comment: Proceedings CNET200

Equivariant configuration spaces

The compression theorem is used to prove results for equivariant configuration spaces that are analogous to the well-known non-equivariant results of May, Milgram and Segal

Positive configuration space

We define and study the totally nonnegative part of the Chow quotient of the Grassmannian, or more simply the nonnegative configuration space. This space has a natural stratification by positive Chow cells, and we show that nonnegative configuration space is homeomorphic to a polytope as a stratified space. We establish bijections between positive Chow cells and the following sets: (a) regular subdivisions of the hypersimplex into positroid polytopes, (b) the set of cones in the positive tropical Grassmannian, and (c) the set of cones in the positive Dressian. Our work is motivated by connections to super Yang-Mills scattering amplitudes, which will be discussed in a sequel.Comment: 46 pages; citations adde