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We present a comprehensive series of dissipationless N-body simulations to investigate the evolution of density distribution in equal-mass mergers between dark matter (DM) halos and multicomponent galaxies. The DM halo models are…
Our main contribution is a concentration inequality for the symmetric volume difference of a $ C^2 $ convex body with positive Gaussian curvature and a circumscribed random polytope with a restricted number of facets, for any probability…
This paper develops a theory of conformal density at infinity for groups with contracting elements. We start by introducing a class of convergence boundary encompassing many known hyperbolic-like boundaries, on which a detailed study of…
Empirical methods for connecting galaxies to their dark matter halos have become essential for interpreting measurements of the spatial statistics of galaxies. In this work, we present a novel approach for parameterizing the degree of…
Dark matter haloes in Lambda CDM simulations grow by mergers with other haloes as well as accretion of "diffuse" non-halo material. We quantify the mass growth rates via these two processes, dM_mer/dt and dM_dif/dt, and their dependence on…
We investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit, when the probability concentrates on weak solutions of a hyperbolic conservation law conservation law. When the…
In his 1910 "Five Variables" paper, Cartan solved the equivalence problem for the geometry of $(2, 3, 5)$ distributions and in doing so demonstrated an intimate link between this geometry and the exceptional simple Lie groups of type…
We show that for a very general class of curvature functions defined in the positive cone, the problem of finding a complete strictly locally convex hypersurface in $H^n+1$ satisfying $f(\kappa)=\sigma\in(0, 1)$ with a prescribed asymptotic…
The rotation velocities of disc galaxies trace dark matter halo structure, providing direct constraints on the galaxy--halo connection. We construct a Bayesian forward model to connect the dark matter halo population predicted by…
We say that a graph G has a perfect H-packing if there exists a set of vertex-disjoint copies of H which cover all the vertices in G. We consider various problems concerning perfect H-packings: Given positive integers n, r, D, we…
A \emph{cylinder packing} is a family of congruent infinite circular cylinders with mutually disjoint interiors in $3$-dimensional Euclidean space. The \emph{local density} of a cylinder packing is the ratio between the volume occupied by…
We use the dispersion measure (DM) and redshift measurements of 24 localized fast radio bursts (FRBs) to compare cosmological models and investigate the Hubble tension. Setting a flat prior on the DM contribution from the Milky Way's halo,…
Recent HST/GHRS observations of the z = 0.7010 absorber toward the QSO 1718+4807 (selected because of apparently ideal characteristics for measuring D/H) yield a D/H significantly higher D/H than some recent high-redshift measurements. Our…
Let $D$ be the ring of $S$-integers in a global field and $\hat{D}$ its profinite completion. We discuss the relation between density in $D$ and the Haar measure of $\hat{D}$: in particular, we ask when the density of a subset $X$ of $D$ is…
In previous work a probabilistic approach to controlling difficulties of density in hyperbolic space led to a workable notion of optimal density for packings of bodies. In this paper we extend an ergodic theorem of Nevo to provide an…
We prove, using elementary methods of complex analysis, the following generalization of the isoperimetric inequality: if $p\in\re$, $\Omega\subset\re^2$ then the inequality $$…
Let $\mathcal{P}$ be a packing of circular disks of radius $\rho>0$ in the Euclidean, spherical, or hyperbolic plane. Let $0\leq\lambda\leq\rho$. We say that $\mathcal{P}$ is a $\lambda$-separable packing of circular disks of radius $\rho$…
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…
The observational fact that the present values of the densities of dark energy and dark matter are of the same order of magnitude, $\rho_{de0}/\rho_{dm0} \sim \mathcal{O}(1)$, seems to indicate that we are currently living in a very special…
Based on sensitive CO measurements from HERACLES and HI data from THINGS, we show that the azimuthally averaged radial distribution of the neutral gas surface density (Sigma_HI + Sigma_H2) in 33 nearby spiral galaxies exhibits a…