Quantum graphs—networks composed of vertices connected by edges on which quantum wave dynamics are defined—have emerged as a versatile model for exploring the interplay between geometry, topology, and ...

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 ...

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 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 ...

This is a preview. Log in through your library . Abstract We consider a linearly edge-reinforced random walk on a class of two-dimensional graphs with constant initial weights. The graphs are obtained ...

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 ...