Related papers: Chernoff's density is log-concave
The central limit theorem for convex bodies says that with high probability the marginal of an isotropic log-concave distribution along a random direction is close to a Gaussian, with the quantitative difference determined asymptotically by…
We establish sharp exponential deviation estimates of the information content as well as a sharp bound on the varentropy for the class of convex measures on Euclidean spaces. This generalizes a similar development for log-concave measures…
Let $\mathcal{P}$ and $\mathbb{N}$ be the sets of all primes and natural numbers, respectively. In this article, it is proved that there has a positive lower density of the natural numbers which can be represented by the form…
We prove Wasserstein contraction of simple slice sampling for approximate sampling w.r.t. distributions with log-concave and rotational invariant Lebesgue densities. This yields, in particular, an explicit quantitative lower bound of the…
We generalize our methodology for computing with Zariski dense subgroups of $\mathrm{SL}(n, \mathbb{Z})$ and $\mathrm{Sp}(n, \mathbb{Z})$, to accommodate input dense subgroups $H$ of $\mathrm{SL}(n, \mathbb{Q})$ and $\mathrm{Sp}(n,…
The massive dark matter halos that host groups and clusters of galaxies have observable properties that appear to be log-normally distributed about power-law mean scaling relations in halo mass. Coupling this assumption with either…
The phenomena of superconductivity and charge density waves are observed in close vicinity in many strongly correlated materials. Increasing evidence from experiments and numerical simulations suggests both phenomena can also occur in an…
The superconducting gap structure of a charge density wave (CDW) superconductor LaPt$_2$Si$_2$ ($T_c$ = 1.6~K) having a quasi two dimensional crystal structure has been investigated using muon spin rotation/relaxation ($\mu$SR) measurements…
We carried out a comprehensive study of the electronic, magnetic, and thermodynamic properties of Ni-doped ZrTe$_2$. High quality Ni$_{0.04}$ZrTe$_{1.89}$ single crystals show a possible coexistence of charge density waves (CDW,…
We investigate for which linear-algebraic groups (over the complex numbers or any local field) there exists subgroups which are dense in the Zariski topology, but discrete in the Hausdorff topology. For instance, such subgroups exist for…
We establish a reversal of Lyapunov's inequality for monotone log-concave sequences, settling a conjecture of Havrilla-Tkocz and Melbourne-Tkocz. A strengthened version of the same conjecture is disproved through counter example. We also…
We carry out a systematic study of the density structure of gas in the Central Molecular Zone (CMZ) in the Galactic center by extracting clumps from the APEX Telescope Large Area Survey of the Galaxy survey at 870 $\mu$m. We find that the…
We present a state-of-the-art x-ray diffraction study of the charge density wave order in 1T-TaS2 as a function of temperature and pressure. Our results prove that the charge density wave, which we characterize in terms of wave vector,…
The presence of different electronic orders other than superconductivity populating the phase diagram of cuprates suggests that they might be the key to disclose the mysteries of this class of materials. In particular charge order in the…
Massive Ultracompact Galaxies (MUGs) are common at z=2-3, but very rare in the nearby Universe. Simulations predict that the few surviving MUGs should reside in galaxy clusters, whose large relative velocities prevent them from merging,…
A family of non-conjugate chaotic maps generalizing the well-known logistic function is defined, and some of its basic properties studied. A simple formula for the Lyapunov exponents of all the maps contained in this family is given based…
We establish upper bounds for tails of order statistics of isotropic log-concave vectors and apply them to derive a concentration of l_r norms of such vectors.
Experimental evidence on high-Tc cuprates reveals ubiquitous charge density wave (CDW) modulations, which coexist with superconductivity. Although the CDW had been predicted by theory, important questions remain about the extent to which…
We establish a result linking the Bouniakowsky conjecture and the density of polynomial roots to prime moduli.
We show that SL(2,R) cocycles with a positive Lyapunov exponent are dense in all regularity classes and for all non-periodic dynamical systems. For Schr\"odinger cocycles, we show prevalence of potentials for which the Lyapunov exponent is…