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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
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