Related papers: Splitting tessellations in spherical spaces
We introduce and study the spherical dimension, a natural topological relaxation of the VC dimension that unifies several results in learning theory where topology plays a key role in the proofs. The spherical dimension is defined by…
In this paper we consider a random partition of the plane into cells, the partition being based on the nodes and links of a {\it random planar geometric graph}. The resulting structure generalises the \emph{random \tes}\ hitherto studied in…
A random planar quadrangulation process is introduced as an approximation for certain cellular automata in terms of random growth of rays from a given set of points. This model turns out to be a particular (rectangular) case of the…
Accurate modelling of redshift-space distortions (RSD) is challenging in the non-linear regime for two-point statistics e.g. the two-point correlation function (2PCF). We take a different perspective to split the galaxy density field…
Mesoscopic density functional theory for inhomogeneous mixtures of sperical particles is developed in terms of mesoscopic volume fractions by a systematic coarse-graining procedure starting form microscopic theory. Approximate expressions…
There are four new structure functions for the spin-1 deuteron in comparison with the ones for the spin-1/2 proton, and they are called $b_1$, $b_2$, $b_3$, and $b_4$. The twist-2 structure functions $b_1$ and $b_2$ are expressed by…
As a step towards a more accurate modelling of redshift-space distortions in galaxy surveys, we develop a general description of the probability distribution function of galaxy pairwise velocities within the framework of the so-called…
We consider a family of random line tessellations of the Euclidean plane introduced in a much more formal context by Hug and Schneider [Geom. Funct. Anal. 17, 156 (2007)] and described by a parameter \alpha\geq 1. For \alpha=1 the zero-cell…
We explain spin structure for a spin-one hadron, in which there are new structure functions, in addition to the ones ($F_1$, $F_2$, $g_1$, $g_2$) which exist for the spin-1/2 nucleon, associated with its tensor structure. The new structure…
Non-Gaussianities of dynamical origin are disentangled from primordial ones using the formalism of large deviation statistics with spherical collapse dynamics. This is achieved by relying on accurate analytical predictions for the one-point…
The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…
We study fractal measures on Euclidean space through the dynamics of "zooming in" on typical points. The resulting family of measures (the "scenery"), can be interpreted as an orbit in an appropriate dynamical system which often…
The fractal dimension of large-scale galaxy clustering has been demonstrated to be roughly $D_F \sim 2$ from a wide range of redshift surveys. If correct, this statistic is of interest for two main reasons: fractal scaling is an implicit…
A generalized version of a well-known problem of D. G. Kendall states that the zero cell of a stationary Poisson hyperplane tessellation in ${\mathbb{R}}^d$, under the condition that it has large volume, approximates with high probability a…
Partitionings (or segmentations) divide a given domain into disjoint connected regions whose union forms again the entire domain. Multi-dimensional partitionings occur, for example, when analyzing parameter spaces of simulation models,…
We present an analytical model for density-split correlation functions, that probe galaxy clustering in different density environments. Specifically, we focus on the cross-correlation between density-split regions and the tracer density…
In this paper we consider spherically symmetric general fluids with heat flux, motivated by causal thermodynamics, and give the appropriate set of conditions that define separating shells defining the divide between expansion and collapse.…
We bridge the properties of the regular square and honeycomb Voronoi tessellations of the plane to those of the Poisson-Voronoi case, thus analyzing in a common framework symmetry-break processes and the approach to uniformly random…
A set of lower bounds on the continuum percolation threshold $\eta_c$ of overlapping convex hyperparticles of general nonspherical (anisotropic) shape with a specified orientational probability distribution in $d$-dimensional Euclidean…
Recent advances in local models for point processes have highlighted the need for flexible methodologies to account for the spatial heterogeneity of external covariates influencing process intensity. In this work, we introduce tessellated…