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 ...

We establish asymptotic vertex degree distribution and examine its relation to the clustering coefficient in two popular random intersection graph models of Godehardt and Jaworski [Electron. Notes ...

We consider a random field {Xij, i, j = 1, ⋯, n} where the random variables Xij takes on values 1 or 0. The collection {Xij} can be viewed as a random graph with nodes {1, ⋯, n} by interpreting Xij = ...

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 ...

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 ...

Expanders graphs are sparse but well-connected. These seemingly contrasting properties have led to many applications in theoretical computer science, from complexity ...