Related papers: Heavy-tailed configuration models at criticality
We study first passage percolation on the configuration model. Assuming that each edge has an independent exponentially distributed edge weight, we derive explicit distributional asymptotics for the minimum weight between two randomly…
Modern risk modelling approaches deal with vectors of multiple components. The components could be, for example, returns of financial instruments or losses within an insurance portfolio concerning different lines of business. One of the…
We propose a novel finite size scaling analysis for percolation transition observed in complex networks. While it is known that cooperative systems in growing networks often undergo an infinite order transition with inverted…
The scaling behavior of the closed trajectories of a moving particle generated by randomly placed rotators or mirrors on a square or triangular lattice is studied numerically. For most concentrations of the scatterers the trajectories close…
We study cluster sizes in supercritical $d$-dimensional inhomogeneous percolation models with long-range edges -- such as long-range percolation -- and/or heavy-tailed degree distributions -- such as geometric inhomogeneous random graphs…
We consider the evolution of scale-free networks according to preferential attachment schemes and show the conditions for which the exponent characterizing the degree distribution is bounded by upper and lower values. Our framework is an…
We consider the rank-1 inhomogeneous random graph in the Brownian regime in the critical window. Aldous studied the weights of the components, and showed that this ordered sequence converges in the $\ell^2$-topology to the ordered…
This paper is organized in three parts closely related to closure properties of heavy-tailed distributions and heavy-tailed random vectors. In the first part we consider two random variables X and Y with distributions F and G respectively.…
Motivated by applications, the last few years have witnessed tremendous interest in understanding the structure as well as the behavior of dynamics for inhomogeneous random graph models. In this study we analyze the maximal components at…
Recently, the scaling limit of cluster sizes for critical inhomogeneous random graphs of rank-1 type having finite variance but infinite third moment degrees was obtained (see previous work by Bhamidi, van der Hofstad and van Leeuwaarden).…
Leaves, i.e., vertices of degree one, can play a significant role in graph structure, especially in sparsely connected settings in which leaves often constitute the largest fraction of vertices. We consider a leaf-based counterpart of the…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
We develop an asymptotic theory for extremes in decomposable graphical models by presenting results applicable to a range of extremal dependence types. Specifically, we investigate the weak limit of the distribution of suitably normalised…
We consider inhomogeneous spatial random graphs on the real line. Each vertex carries an i.i.d. weight and edges are drawn such that short edges and edges to vertices with large weights occur with higher probability. This allows the study…
We consider the random directed graph $\vec{G}(n,p)$ with vertex set $\{1,2,\ldots,n\}$ in which each of the $n(n-1)$ possible directed edges is present independently with probability $p$. We are interested in the strongly connected…
Heavy-tailed phenomena appear across diverse domains --from wealth and firm sizes in economics to network traffic, biological systems, and physical processes-- characterized by the disproportionate influence of extreme values. These…
We study the susceptibility, i.e., the mean cluster size, in random graphs with given vertex degrees. We show, under weak assumptions, that the susceptibility converges to the expected cluster size in the corresponding branching process. In…
We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…
Consider balls $\Lambda_n$ of growing volumes in the $d$-dimensional hierarchical lattice, and place edges independently between each pair of vertices $x\neq y\in\Lambda_n$ with probability $1-\exp(-\beta J(x, y) )$ where $J(x, y) \asymp \|…
We consider a new approach in the definition of two-dimensional heavy-tailed distributions. Namely, we introduce the classes of two-dimensional long-tailed, of twodimensional dominatedly varying and of two-dimensional consistently varying…