Related papers: Concentration inequalities for Paley-Wiener spaces
An affine version of the linear subspace concentration inequality as proposed by Wu is established for centered convex bodies. This generalizes results from Wu and Freyer, Henk, Kipp on polytopes to convex bodies.
I re-examine the relation between virial mass and concentration for groups and clusters of galaxies as measured in a number of recent works. As previously noted by several authors, low-mass clusters and groups of galaxies display…
One of the basic problems in discrete geometry is to determine the most efficient packing of congruent replicas of a given convex set $K$ in the plane or in space. The most commonly used measure of efficiency is density. Several types of…
We summarize recent works on the question of the nucleon mass decomposition and the 2D relativistic distribution of pressure forces on the light front. All these mechanical properties are encoded in the energy-momentum tensor of the system…
We introduce a new generalization of relative entropy to non-negative vectors with sums $\gt 1$. We show in a purely combinatorial setting, with no probabilistic considerations, that in the presence of linear constraints defining a convex…
We use the Allen et al. (2004) Chandra measurements of x-ray gas mass fraction of 26 rich clusters to place constraints on the scalar-field dark energy model with inverse power law potential energy density. The constraints are consistent…
We show that any subset of the natural numbers with positive logarithmic Banach density contains a set that is within a factor of two of a geometric progression, improving the bound on a previous result of the authors. Density conditions on…
New Vapnik and Chervonenkis type concentration inequalities are derived for the empirical distribution of an independent random sample. Focus is on the maximal deviation over classes of Borel sets within a low probability region. The…
The mass-concentration relation of dark matter halos reflects the assembly history of objects in hierarchical structure formation scenarios, and depends on fundamental quantities in cosmology such as the slope of the primordial matter…
A family of m independent identically distributed random variables indexed by a chemical potential \phi\in[0,\gamma] represents piles of particles. As \phi increases to \gamma, the mean number of particles per site converges to a maximal…
It is well known that a spherically symmetric compact star whose energy density decreases monotonically possesses an upper bound on its mass-to-radius ratio, $2M/R\leq 8/9$. However, field configurations typically will not be compact. Here…
The expected sensitivity of cluster SZ number counts to neutrino mass in the sub-eV range is assessed. We find that from the ongoing {\it Planck}/SZ measurements the (total) neutrino mass can be determined at a (1-sigma) precision of 0.06…
Measurements of the evolution with redshift of the number density of massive galaxy clusters are used to constrain the energy density of massive neutrinos and so the sum of neutrino masses $\sum m_\nu$. We consider a spatially-flat…
Influence of volume capture on a process of volume reflection of ultrarelativistic particles moving in bent single crystals was considered analytically. Relations describing various distributions of particles involving in the process, the…
Many statistics of roots of random polynomials have been studied in the literature, but not much is known on the concentration aspect. In this note we present a systematic study of this question, aiming towards nearly optimal bounds to some…
A 1965 problem due to Danzer asks whether there exists a set with finite density in Euclidean space intersecting any convex body of volume one. A suitable weakening of the volume constraint leads to the (much more recent) problem of…
The recently suggested notion of total mass density for closed universes is extended to closed universes with a positive cosmological constant. Assuming that the matter fields satisfy the dominant energy condition, it is shown that the…
Statistical measures of galaxy clusters are sensitive to neutrino masses in the sub-eV range. We explore the possibility of using cluster number counts from the ongoing PLANCK/SZ and future cosmic-variance-limited surveys to constrain…
We consider a random model of diffusion and coagulation. A large number of small particles are randomly scattered at an initial time. Each particle has some integer mass and moves in a Brownian motion whose diffusion rate is determined by…
If the cosmological limits on the sum of the neutrino masses are taken seriously we have first measurements of the masses of the neutrinos. Using the Planck experiment's limit $\sum_{i=1}^3{m_i} < 230 ~meV$ and some simple assumptions on…