Related papers: Robust Morphological Measures for Large-Scale Stru…
This is intended as an analysis of the global properties of static and stationary spacetimes with complete (timelike) Killing field, with particular attention to quotients by group actions. This is presented in terms of algebraic structures…
Three methods for detecting and characterizing structure in point data, such as that generated by redshift surveys, are described: classification using self-organizing maps, segmentation using Bayesian blocks, and density estimation using…
We study random composite structures considered up to symmetry that are sampled according to weights on the inner and outer structures. This model may be viewed as an unlabelled version of Gibbs partitions and encompasses multisets of…
Open cellular solids usually possess random microstructures that may contain a characteristic length scale, such as the cell size. This gives rise to size dependent mechanical properties where large systems behave differently from small…
To which degree are shape indices of individual cells of a tessellation characteristic for the stochastic process that generates them? Within the context of stochastic geometry and the physics of disordered materials, this corresponds to…
We describe and test a method to quantitatively classify clusters of galaxies according to their projected morphologies. This method will be subsequently used to place constraints on cosmological parameters ($\Omega$ and the power spectrum…
The study of galaxies has changed dramatically over the past few decades with the advent of large-scale astronomical surveys. These large collaborative efforts have made available high-quality imaging and spectroscopy of hundreds of…
The Minkowski content $L_0(G)$ of a body $G\subset{\mathbb{R}}^d$ represents the boundary length (for $d=2$) or the surface area (for $d=3$) of $G$. A method for estimating $L_0(G)$ is proposed. It relies on a nonparametric estimator based…
On the class of log-concave functions on $\R^n$, endowed with a suitable algebraic structure, we study the first variation of the total mass functional, which corresponds to the volume of convex bodies when restricted to the subclass of…
The Minkowski problem in convex geometry concerns showing that a given Borel measure on the unit sphere is, up to perhaps a constant, some type of surface area measure of a convex body. Two types of Minkowski problems in particular are an…
We study topological properties of large scale structure in a set of scale free N-body simulations using the genus and percolation curves as topological characteristics. Our results show that as gravitational clustering advances, the…
Lecture notes in Russian. Topics: the Haar measure (abstract theorems and explicit descriptions for different groups), measures on infinite-dimensional spaces with large natural groups of symmetries (Gaussian measures, Poisson measures,…
In this article we extend the notion of metric measure spaces to so-called metric two-level measure spaces (m2m spaces): An m2m space $(X, r, \nu)$ is a Polish metric space $(X, r)$ equipped with a two-level measure $\nu \in…
Cosmic structures at large scales represent the earliest and most extended form of matter condensation. In this lecture we review the application of the methods and concepts of modern statistical physics to these structures. This leads to a…
The thesis deals with recognizing diffeomorphisms from fractal properties of discrete orbits, generated by iterations of such diffeomorphisms. The notion of fractal properties of a set refers to the box dimension, the Minkowski content and…
U-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Ito…
The aim of our work is to analyze size distributions of particles and their agglomerates in imagery from astrophysical microgravity experiments. The data acquired in these experiments are given by sequences consisting of several hundred…
By virtue of their high galaxy space densities and their large spatial separations, clusters are efficient and accurate tracers of the large-scale density and velocity fields. Substantial progress has been made over the past decade in the…
Voronoi tessellations of Poisson point processes are widely used for modeling many types of physical and biological systems. In this paper, we analyze simulated Poisson-Voronoi structures containing a total of 250,000,000 cells to provide…
In this paper we study physical measures for $\C^{1+\alpha}$ partially hyperbolic diffeomorphisms with mostly expanding center. We show that every diffeomorphism with mostly expanding center direction exhibits a geometrical-combinatorial…