The Annals of Applied Probability, Vol. 28, No. 4 (August 2018), pp. 2003-2062 (60 pages) Given a graph, the popular “modularity” clustering method specifies a partition of the vertex set as the ...

Vertices arrive sequentially in space and are joined to existing vertices at random according to a preferential rule combining degree and spatial proximity. We investigate phase transitions in the ...

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 ...

Stochastic processes form the backbone of modern probability theory, describing systems that evolve randomly over time or space. They are instrumental in areas ranging from statistical physics to ...