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 ...

The Annals of Applied Probability, Vol. 16, No. 1 (Feb., 2006), pp. 295-309 (15 pages) We consider the discrete Laplace operator $\Delta ^{(N)}$ on Erdős-Rényi random graphs with N vertices and edge ...

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 ...