Random Matrix Theory (RMT) has emerged as an indispensable framework for understanding the statistical properties of matrices whose entries are determined by probabilistic processes. Initially ...

This is a preview. Log in through your library . Abstract We derive the full phase diagram for a large family of two-parameter exponential random graph models, each containing a first order transition ...

This lecture course is devoted to the study of random geometrical objects and structures. Among the most prominent models are random polytopes, random tessellations, particle processes and random ...

Abstract: Given a (monotone) graph property P and a random graph G(n,m) with n vertices and m edges, typically, there is a value m(n) such that P holds (does not hold) with probability approaching 1 ...

When the mathematicians Jeff Kahn and Gil Kalai first posed their “expectation threshold” conjecture in 2006, they didn’t believe it themselves. Their claim — a broad assertion about mathematical ...

Scientists are exploring a mysterious pattern, found in birds’ eyes, boxes of marbles and other surprising places, that is neither regular nor random. All complex correlated systems, from Arctic melt ...