We consider long-range Bernoulli bond percolation on the $ d $-dimensional hierarchical
lattice in which each pair of points $ x $ and $ y $ are connected by an edge with probability …

Consider a uniform rooted Cayley tree T n with n vertices and let m cars arrive sequentially,
independently, and uniformly on its vertices. Each car tries to park on its arrival node, and if …

We consider a natural model of inhomogeneous random graphs that extends the classical
Erdős–Rényi graphs and shares a close connection with the multiplicative coalescence, as …

We establish uniform sub-exponential tail bounds for the width, height and maximal
outdegree of critical Bienaymé–Galton–Watson trees conditioned on having a large fixed …

We study the critical behavior of the component sizes for the configuration model when the
tail of the degree distribution of a randomly chosen vertex is a regularly-varying function with …

The last few years have witnessed tremendous interest in understanding the structure as
well as the behavior of dynamics for inhomogeneous random graph models to gain insight …

In this book, we discuss stochastic processes on random graphs. The understanding of such
processes is interesting from an applied perspective, since random graphs serve as models …

We prove a metric space scaling limit for a critical random graph with independent and
identically distributed degrees having power-law tail behaviour with exponent $\alpha+ 1 …

We prove a metric space scaling limit for a critical random graph with independent and
identically distributed degrees having power-law tail behaviour with exponent α+ 1, where …

We study limits of the largest connected components (viewed as metric spaces) obtained by
critical percolation on uniformly chosen graphs and configuration models with heavy-tailed …