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Probability Seminar

Event Type
Seminar/Symposium
Sponsor
Department of Mathematics
Location
347 Altgeld Hall
Date
Dec 6, 2022   2:00 - 2:50 pm  
Speaker
David Clancy, Wisconsin-Madison
Contact
Partha Dey
Views
39
Title:   Component sizes of degree-corrected stochastic blockmodel
 
Abstract:    The stochastic block model (SBM) is a simple probabilistic model for graphs that exhibit clustering. Each vertex is assigned a type i = 1, 2, ..., m, and edges are included independently with probability depending on the types of the two incident vertices. The degree-corrected SBM (DCSBM) exhibits similar clustering behavior but allows for inhomogeneous degree distributions. The sizes of connected components for these graph models are poorly understood unless m = 1 or the SBM is a random bipartite graph. In this talk, we'll see that under fairly general conditions, the asymptotic sizes of connected components in the DCSBM can be precisely described in terms of a multiparameter and multidimensional random field. Not only that, but we can describe the asymptotic proportion of vertices of each type in each of the macroscopic connected components. This talk is based on joint work with Vitalii Konarovskyi and Vlada Limic.
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