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We study a family of directed random graphs whose arcs are sampled independently of each other, and are present in the graph with a probability that depends on the attributes of the vertices involved. In particular, this family of models includes as special cases the direct
We study the typical behavior of a generalized version of Googles PageRank algorithm on a large family of inhomogeneous random digraphs. This family includes as special cases direct
We study random digraphs on sequences of expanders with bounded average degree and weak local limit. The threshold for the existence of a giant strongly connected component, as well as the asymptotic fraction of nodes with giant fan-in or giant fan-o
The voter model is a classical interacting particle system modelling how consensus is formed across a network. We analyse the time to consensus for the voter model when the underlying graph is a subcritical scale-free random graph. Moreover, we gener
We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, $Wsim N$. All previous results concerning universality of no
Consider a set of $n$ vertices, where each vertex has a location in $mathbb{R}^d$ that is sampled uniformly from the unit cube in $mathbb{R}^d$, and a weight associated to it. Construct a random graph by placing edges independently for each vertex pa