Related papers: Peaks over Threshold in Scale-Free Random Graphs
We introduce and analyze a class of growing geometric random graphs that are invariant under rescaling of space and time. Directed connections between nodes are drawn according to influence zones that depend on node position in space and…
Consider a binary mixture model of the form $F_\theta = (1-\theta)F_0 + \theta F_1$, where $F_0$ is standard Gaussian and $F_1$ is a completely specified heavy-tailed distribution with the same support. For a sample of $n$ independent and…
The $\boldsymbol{\beta}$-model for random graphs is commonly used for representing pairwise interactions in a network with degree heterogeneity. Going beyond pairwise interactions, Stasi et al. (2014) introduced the hypergraph…
Modelling excesses over a high threshold using the Pareto or generalized Pareto distribution (PD/GPD) is the most popular approach in extreme value statistics. This method typically requires high thresholds in order for the (G)PD to fit…
In this paper, we consider an analog of the well-studied extremal problem for triangle-free subgraphs of graphs for uniform hypergraphs. A loose triangle is a hypergraph $T$ consisting of three edges $e,f$ and $g$ such that $|e \cap f| = |f…
We propose a random graph model with preferential attachment rule and \emph{edge-step functions} that govern the growth rate of the vertex set. We study the effect of these functions on the empirical degree distribution of these random…
Both empirical and theoretical investigations of scale-free network models have found that large degrees in a network exert an outsized impact on its structure. However, the tools used to infer the tail behavior of degree distributions in…
Extreme events can come either from point processes, when the size or energy of the events is above a certain threshold, or from time series, when the intensity of a signal surpasses a threshold value. We are particularly concerned by the…
In this article, we consider a configuration of weighted random balls in $\mathbb{R}^d$ generated according to a Poisson point process. The model investigated exhibits inhomogeneity, as well as dependence between the centers and the radii…
The Peaks Over Threshold (POT) method is the most popular statistical method for the analysis of univariate extremes. Even though there is a rich applied literature on Bayesian inference for the POT, the asymptotic theory for such proposals…
Let K be a convex set in R d and let K $\lambda$ be the convex hull of a homogeneous Poisson point process P $\lambda$ of intensity $\lambda$ on K. When K is a simple polytope, we establish scaling limits as $\lambda$ $\rightarrow$ $\infty$…
We study random subgraphs of an arbitrary finite connected transitive graph $\mathbb G$ obtained by independently deleting edges with probability $1-p$. Let $V$ be the number of vertices in $\mathbb G$, and let $\Omega$ be their degree. We…
Metocean extremes often vary systematically with covariates such as direction and season. In this work, we present non-stationary models for the size and rate of occurrence of peaks over threshold of metocean variables with respect to one-…
In a random graph, counts for the number of vertices with given degrees will typically be dependent. We show via a multivariate normal and a Poisson process approximation that, for graphs which have independent edges, with a possibly…
We propose a random bipartite graph with weights assigned to both parts of the vertex sets. Edges are formed independently with probabilities that depend on these weights. This bipartite graph naturally gives rise to a random intersection…
Given a weighted graph $G$, a $(\beta,\varepsilon)$-hopset $H$ is an edge set such that for any $s,t \in V(G)$, where $s$ can reach $t$ in $G$, there is a path from $s$ to $t$ in $G \cup H$ which uses at most $\beta$ hops whose length is in…
We argue that the freezing transition scenario, previously conjectured to occur in the statistical mechanics of 1/f-noise random energy models, governs, after reinterpretation, the value distribution of the maximum of the modulus of the…
A bootstrap percolation process on a graph $G$ is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least $r$ infected neighbours…
Consider the classical $(2+1)$-dimensional Solid-On-Solid model above a hard wall on an $L\times L$ box of $\bbZ^2$. The model describes a crystal surface by assigning a non-negative integer height $\eta_x$ to each site $x$ in the box and 0…
Let $\Delta\subsetneq\V$ be a proper subset of the vertices $\V$ of the defining graph of an irreducible and aperiodic shift of finite type $(\Sigma_{A}^{+},\S)$. Let $\Sigma_{\Delta}$ be the subshift of allowable paths in the graph of…