Related papers: Tessellation-valued processes that are generated b…
Until now, little was known about properties of small cells in a Poisson hyperplane tessellation. The few existing results were either heuristic or applying only to the two dimensional case and for very specific size functionals and…
The spatial cosmic matter distribution on scales of a few up to more than a hundred Megaparsec displays a salient and pervasive foamlike pattern. Voronoi tessellations are a versatile and flexible mathematical model for such weblike spatial…
We consider the behavior of spatial point processes when subjected to a class of linear transformations indexed by a variable T. It was shown in Ellis [Adv. in Appl. Probab. 18 (1986) 646-659] that, under mild assumptions, the transformed…
The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre…
We consider stochastic point processes generating time series exhibiting power laws of spectrum and distribution density (Phys. Rev. E 71, 051105 (2005)) and apply them for modeling the trading activity in the financial markets and for the…
Asymptotic properties of finitely generated subgroups of free groups, and of finite group presentations, can be considered in several fashions, depending on the way these objects are represented and on the distribution assumed on these…
We show an efficient algorithm for generating geodesic regular tree structures for periodic hyperbolic and Euclidean tessellations and experimentally verify its performance on tessellations.
This paper is focused on a class of spatial birth and death process of the Euclidean space where the birth rate is constant and the death rate of a given point is the shot noise created at its location by the other points of the current…
The work continues the author's many-year research in theory of maximal branching processes, which are obtained from classical branching processes by replacing the summation of descendant numbers with taking the maximum. One can say that in…
The Mellin transform is usually applied in probability theory to the product of independent random variables. In recent times the machinery of the Mellin transform has been adopted to describe the L\'evy stable distributions, and more…
It was recently noticed that high-energy scattering processes in QCD have a stochastic nature. An event-by-event scattering amplitude is characterised by a saturation scale which is a random variable. The statistical ensemble of saturation…
We construct a random partition of the space-time plane $\mathbb{R}_+\times \mathbb{R}$ using two coupled stochastic squared Bessel flows, whose parameters differ by $\delta\in (0,2)$. We show that the cells of this partition correspond to…
Isogenic Escherichia coli growing exponentially in a constant environment display large variation in growth-rates, division-sizes and generation-times. It is unclear how these seemingly random cell cycles can be reconciled with the precise…
This paper develops methods to study the distribution of Eulerian statistics defined by second-order recurrence relations. We define a random process to decompose the statistics over compositions of integers. It is shown that the numbers of…
Maintenance and regeneration of adult tissues rely on the self-renewal of stem cells. Regeneration without over-proliferation requires precise regulation of the stem cell proliferation and differentiation rates. The nature of such…
We study a coarsening process of one-dimensional cell complexes. We show that if cell boundaries move with velocities proportional to the difference in size of neighboring cells, then the average cell size grows at a prescribed exponential…
Modelling, analysing and inferring triggering mechanisms in population reproduction is fundamental in many biological applications. It is also an active and growing research domain in mathematical biology. In this chapter, we review the…
For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met, the…
This paper deals with the typical cell in a Poisson line tessellation in the plane whose directional distribution is concentrated on three equally spread values with possibly different weights. Such a random polygon can only be a triangle,…
A regular sampling theory in a multiply generated unitary invariant subspace of a separable Hilbert space $\mathcal{H}$ is proposed. This subspace is associated to a unitary representation of a countable discrete abelian group $G$ on…