Related papers: On the behavior of extreme $d$-dimensional spatial…
A finite set of unlabelled points in Euclidean space is the simplest representation of many real objects from mineral rocks to sculptures. Since most solid objects are rigid, their natural equivalence is rigid motion or isometry maintaining…
Spherical symmetry arguments are used to produce a general device to convert identities and inequalities for the $p$th absolute moments of real-valued random variables into the corresponding identities and inequalities for the $p$th moments…
Kendall's Shape Theory covers shapes formed by $N$ points in $\mathbb{R}^d$ upon quotienting out the similarity transformations. This theory is based on the geometry and topology of the corresponding configuration space: shape space.…
We examine the hypothesis that space-time is a product of a continuous four-dimensional manifold times a finite space. A new tensorial notation is developed to present the various constructs of noncommutative geometry. In particular, this…
This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in $\mathbb{R}^3$,…
We analyze two models of random geometries~: planar hyper-cubic random surfaces and four dimensional simplicial quantum gravity. We show for the hyper-cubic random surface model that a geometrical constraint does not change the critical…
Extreme events over large spatial domains may exhibit highly heterogeneous tail dependence characteristics, yet most existing spatial extremes models yield only one dependence class over the entire spatial domain. To accurately characterize…
Modelling the extremal dependence structure of spatial data is considerably easier if that structure is stationary. However, for data observed over large or complicated domains, non-stationarity will often prevail. Current methods for…
R. Pavlov and S. Schmieding provided recently some results about generic $\mathbb{Z}$-shifts, which rely mainly on an original theorem stating that isolated points form a residual set in the space of $\mathbb{Z}$-shifts such that all other…
A uniform bounded variation estimate for finite volume approximations of the nonlinear scalar conservation law $\partial_t \alpha + \mathrm{div}(\boldsymbol{u}f(\alpha)) = 0$ in two and three spatial dimensions with an initial data of…
Employing numerical and theoretical methods, we investigate the structural characteristics of random sequential addition (RSA) of congruent spheres in $d$-dimensional Euclidean space $\mathbb{R}^d$ in the infinite-time or saturation limit…
Statistical methods for inference on spatial extremes of large datasets are yet to be developed. Motivated by standard dimension reduction techniques used in spatial statistics, we propose an approach based on empirical basis functions to…
The conditional extremes framework allows for event-based stochastic modeling of dependent extremes, and has recently been extended to spatial and spatio-temporal settings. After standardizing the marginal distributions and applying an…
We study "random surfaces," which are random real (or integer) valued functions on Z^d. The laws are determined by convex, nearest neighbor, difference potentials that are invariant under translation by a full-rank sublattice L of Z^d; they…
We analyze the accuracy of the discrete least-squares approximation of a function $u$ in multivariate polynomial spaces $\mathbb{P}_\Lambda:={\rm span} \{y\mapsto y^\nu \,: \, \nu\in \Lambda\}$ with $\Lambda\subset \mathbb{N}_0^d$ over the…
Non-stationary extremal dependence, whereby the relationship between the extremes of multiple variables evolves over time, is commonly observed in many environmental and financial data sets. However, most multivariate extreme value models…
Let X be a symmetric space of non-compact type or a locally finite, strongly transitive Euclidean building, and let B denote the geodesic boundary of X. We reduce the study of visual limits of maximal flats in X to the study of limits of…
Several new geometric quantile-based measures for multivariate dispersion, skewness, kurtosis, and spherical asymmetry are defined. These measures differ from existing measures, which use volumes and are easy to calculate. Some theoretical…
We introduce the concept of geometric extremal graphical models, which are defined through the gauge function of the limit set obtained from suitably scaled random vectors in light-tailed margins. For block graphs, we prove results relating…
We construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial…