5,648 research outputs found
Modeling heterogeneity in random graphs through latent space models: a selective review
We present a selective review on probabilistic modeling of heterogeneity in
random graphs. We focus on latent space models and more particularly on
stochastic block models and their extensions that have undergone major
developments in the last five years
Morphisms of Berkovich curves and the different function
Given a generically \'etale morphism of quasi-smooth
Berkovich curves, we define a different function
that measures the wildness of the topological ramification locus of . This
provides a new invariant for studying , which cannot be obtained by the
usual reduction techniques. We prove that is a piecewise monomial
function satisfying a balancing condition at type 2 points analogous to the
classical Riemann-Hurwitz formula, and show that can be used to
explicitly construct the simultaneous skeletons of and . As an
application, we use our results to completely describe the topological
ramification locus of when its degree equals to the residue characteristic
.Comment: Final version, 49 pages, to appear in Adv.Mat
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