We study the problem of community detection in a random hypergraph model which we call
the stochastic block model for $ k $-uniform hypergraphs ($ k $-SBM). We investigate the …

During the past decade or so, there has been much interest in generating and analyzing
graphs resembling large-scale real-world networks such as the world wide web, neural …

In this article, we prove new inequalities between some common probability metrics. Using
these inequalities, we obtain novel local limit theorems for the magnetization in the Curie …

The phase transition in the size of the giant component in random graphs is one of the most
well‐studied phenomena in random graph theory. For hypergraphs, there are many possible …

In this paper, we prove a local limit theorem for the distribution of the number of triangles in
the Erdos‐Rényi random graph G (n, p), where is a fixed constant. Our proof is based on …

The theory of random graphs deals with asymptotic properties of graphs equipped with a
certain probability distribution; for example, it studies how the component structure of a …

Local Limit Theorems for the Giant Component of Random Hypergraphs Page 1 Combinatorics,
Probability and Computing (2014) 23, 331–366. c Cambridge University Press 2014 …

In this paper we consider j-tuple-connected components in random k-uniform hypergraphs
(the j-tuple-connectedness relation can be defined by letting two j-sets be connected if they …

Recently, we adapted random walk arguments based on work of Nachmias and Peres,
Martin‐Löf, Karp and Aldous to give a simple proof of the asymptotic normality of the size of …

This article discusses random hypergraphs with varying hyperedge sizes, admitting large
hyperedges with size tending to infinity, and heavy-tailed limiting hyperedge size …