Related papers: Distribution and Dependence of Extremes in Network…
For any finite colored graph we define the empirical neighborhood measure, which counts the number of vertices of a given color connected to a given number of vertices of each color, and the empirical pair measure, which counts the number…
In many practical applications, evaluating the joint impact of combinations of environmental variables is important for risk management and structural design analysis. When such variables are considered simultaneously, non-stationarity can…
Assessing the probability of occurrence of extreme events is a crucial issue in various fields like finance, insurance, telecommunication or environmental sciences. In a multivariate framework, the tail dependence is characterized by the…
We consider the clustering of extremes for stationary regularly varying random fields over arbitrary growing index sets. We study sufficient assumptions on the index set such that the limit of the point random fields of the exceedances…
Davis and Mikosch [7] introduced the extremogram as a flexible quantitative tool for measuring various types of extremal dependence in a stationary time series. There we showed some standard statistical properties of the sample extremogram.…
Exponential random graph models (ERGMs) are widely used for modeling social networks observed at one point in time. However the computational difficulty of ERGM parameter estimation has limited the practical application of this class of…
A class of random graph models is considered, combining features of exponential-family models and latent structure models, with the goal of retaining the strengths of both of them while reducing the weaknesses of each of them. An open…
Background: Recently developed techniques to study the spread of infectious diseases through networks make assumptions that the initial proportion infected is infinitesimal and the population behavior is static throughout the epidemic. The…
Modelling dependencies between climate extremes is important for climate risk assessment, for instance when allocating emergency management funds. In statistics, multivariate extreme value theory is often used to model spatial extremes.…
We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- direct cascading or fragmentation, spatial dynamics, and external driving -- are combined in a classical age-dependent…
Extreme events such as earthquakes, floods, and power blackouts often display burst phenomena where multiple extreme events occur in quick succession or in bunches. This study examines bunching of extreme events on a complex network using a…
We investigate a branching random walk where the displacements are independent from the branching mechanism and have a stretched exponential distribution. We describe the positions of the particles in the vicinity of the rightmost particle…
Graphical models in extremes have emerged as a diverse and quickly expanding research area in extremal dependence modeling. They allow for parsimonious statistical methodology and are particularly suited for enforcing sparsity in…
Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…
Nowadays there is a multitude of measures designed to capture different aspects of network structure. To be able to say if the structure of certain network is expected or not, one needs a reference model (null model). One frequently used…
Inference over tails is performed by applying only the results of extreme value theory. Whilst such theory is well defined and flexible enough in the univariate case, multivariate inferential methods often require the imposition of…
It is no secret that statistical modelling often involves making simplifying assumptions when attempting to study complex stochastic phenomena. Spatial modelling of extreme values is no exception, with one of the most common such…
We consider stationary configurations of points in Euclidean space which are marked by positive random variables called scores. The scores are allowed to depend on the relative positions of other points and outside sources of randomness.…
We examine the stationary distribution of random walks on directed graphs. In particular, we focus on the {\em principal ratio}, which is the ratio of maximum to minimum values of vertices in the stationary distribution. We give an upper…
Random walk on discrete lattice models is important to understand various types of transport processes. The extreme events, defined as exceedences of the flux of walkers above a prescribed threshold, have been studied recently in the…