Related papers: Second order concentration on the sphere
Let $F$ be a Hecke-Maa\ss\ cusp form for $\mathrm{SL}(3,\mathbb{Z})$. We obtain the first non-trivial upper bound of the second moment of $L(F,s)$ in $t$-aspect: $$\int_{T}^{2T}|L(F,1/2+it)|^2 dt\ll_{F,\varepsilon}…
Motivated by the study of an important data set for understanding the large-scale structure of the universe, this work considers the estimation of the reduced second moment function, or K-function, of a stationary point process observed…
Two-sided bounds are explored for concentration functions and R\'enyi entropies in the class of discrete log-concave probability distributions. They are used to derive certain variants of the entropy power inequalities.
Simulations for the density and potential profiles of the ions in the planar electrical double layer of a model electrolyte or an ionic liquid are reported. The ions of a real electrolyte or an ionic liquid are usually not spheres; in ionic…
Equations of motion of spinning density for extended objects, and corresponding deviation equations are derived. The problem of motion for a variable mass to a spinning extended object is obtained. Spinning fluids may be considered as a…
We prove the existence of an abundance of new Einstein metrics on odd dimensional spheres including exotic spheres, many of them depending on continuous parameters. The number of families as well as the number of parameter grows double…
We derive concentration inequalities for functions of the empirical measure of large random matrices with infinitely divisible entries and, in particular, stable ones. We also give concentration results for some other functionals of these…
The fundamental measure density functional theory for hard spheres is generalized to binary mixtures of arbitrary positive and moderate negative non-additivity between unlike components. In bulk the theory predicts fluid-fluid phase…
We implement Lie transform perturbation theory to second order for the planar spin-orbit problem. The perturbation parameter is the asphericity of the body, with the orbital eccentricity entering as an additional parameter. We study first…
Understanding how particles are arranged on the sphere is not only central to numerous physical, biological, and materials systems but also finds applications in mathematics and in analysis of geophysical and meteorological measurements. In…
We derive out naturally some important distributions such as high order normal distributions and high order exponent distributions and the Gamma distribution from a geometrical way. Further, we obtain the exact mean-values of integral form…
We develop a systematic framework for constructing spherical harmonics on the two-dimensional unit sphere as superpositions of Gaussian beams whose poles form well-separated point configurations. The distributional and analytic properties…
Starting from concentration of measure hypotheses on $m$ random vectors $Z_1,\ldots, Z_m$, this article provides an expression of the concentration of functionals $\phi(Z_1,\ldots, Z_m)$ where the variations of $\phi$ on each variable…
The concept of splitting tessellations and splitting tessellation processes in spherical spaces of dimension $d\geq 2$ is introduced. Expectations, variances and covariances of spherical curvature measures induced by a splitting…
The nonzero level sets of a homogeneous, logarithmically homogeneous, or translationally homogeneous function are affine spheres if and only if the Hessian determinant of the function is a multiple of a power or an exponential of the…
We investigate the relation between the concentration and the product of metric measure spaces. We have the natural question whether, for two concentrating sequences of metric measure spaces, the sequence of their product spaces also…
In this paper, we establish the curvature estimates for a class of Hessian type equations. Some applications are also discussed.
We obtain existence and uniqueness for odd second order oscillators in the space of odd functions without topological assumptions on the nonlinear part.
In this paper we show a new inequality which generalizes to the unit sphere the Lebedev-Milin inequality of the exponentiation of functions on the unit circle. It may also be regarded as the counterpart on the sphere of the second…
In this article, the possibility of generating non-classical light due to Planck-scale effects is considered. For this purpose, a widely studied model of deformation of the Heisenberg uncertainty relation is applied to single-mode and…