Related papers: Comparisons and asymptotics for empty space hazard…
The topic of this survey are geometric functionals of a Boolean model (in Euclidean space) governed by a stationary Poisson process of convex grains. The Boolean model is a fundamental benchmark of stochastic geometry and continuum…
An occupancy problem with an infinite number of bins and a random probability vector for the locations of the balls is considered. The respective sizes of bins are related to the split times of a Yule process. The asymptotic behavior of the…
We investigate experimentally the statistics of the free volume inside bidimensional granular packings, for two different kinds of grains and two levels of compaction. With the aim to gain new insight into the statistical description of…
We study the Poisson Boolean model where the grains are random convex bodies with a rotation-invariant distribution. We say that a grain distribution is dense if the union of the grains covers the entire space and robust if the union of the…
We study the effective behavior of heterogeneous energies arising in the modeling of material voids in geometrically linear elastic materials. Specifically, we consider functionals featuring bulk terms depending on the symmetrized gradient…
A number of recent studies have estimated the inter-galactic void probability function and investigated its departure from various random models. We study a family of parametric statistical models based on gamma distributions, which do give…
This paper deals with the union set of a stationary Poisson process of cylinders in $\mathbb{R}^n$ having an $(n-m)$-dimensional base and an $m$-dimensional direction space, where $m\in\{0,1,\ldots,n-1\}$ and $n\geq 2$. The concept…
This paper describes a compound Poisson-based random effects structure for modeling zero-inflated data. Data with large proportion of zeros are found in many fields of applied statistics, for example in ecology when trying to model and…
Context: Bouncing collisions of dust aggregates within the protoplanetary may have a significant impact on the growth process of planetesimals. Yet, the conditions that result in bouncing are not very well understood. Existing simulations…
In this chapter we review some examples, methods, and recent results involving comparison of clustering properties of point processes. Our approach is founded on some basic observations allowing us to consider void probabilities and moment…
For two decades now, the importance of microstructure in the mechanical behaviour of a large collection of grains has been a topic of intense research. Many approaches have been developed to study the microstructure in granular materials,…
Understanding the collisional behavior of dust aggregates is essential in the context of planet formation. It is known that low-velocity collisions of dust aggregates result in bouncing rather than sticking when the filling factor of…
The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between…
The clustering of galaxies in ongoing and upcoming galaxy surveys contains a wealth of cosmological information, but extracting this information is a non-trivial task since galaxies and their host haloes are stochastic tracers of the matter…
Although impurities are unavoidable in real-world and experimental systems, most numerical studies on nucleation focus on pure (impurity-free) systems. As a result, the role of impurities in phase transitions remains poorly understood,…
There is currently a gap in theory for point patterns that lie on the surface of objects, with researchers focusing on patterns that lie in a Euclidean space, typically planar and spatial data. Methodology for planar and spatial data thus…
We study a family of parametric statistical models based on gamma distributions, which do give realistic descriptions for other stochastic porous media. Gamma distributions contain as a special case the exponential distributions, which…
This dissertation develops, for several families of statistical mechanical and random growth models, techniques for analyzing infinite-volume asymptotics. In the statistical mechanical setting, we focus on the low-temperature phases of spin…
Granular materials are involved in most industrial and environmental processes, as well as many civil engineering applications. Although significant advances have been made in understanding the statics and dynamics of cohesionless grains…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…