Related papers: Remarks on the error term in Chebotarev Density Th…
In this paper, we derive new probability bounds for Chebyshev's inequality if the supremum of the probability density function is known. This result holds for one-dimensional or multivariate continuous probability distributions with finite…
A theory of $\infty$-Besov capacities is developed and several applications are provided. In particular, we solve an open problem in the theory of limits of the $\infty$-Besov semi-norms, we obtain new restriction-extension inequalities and…
For manifolds with a distinguished asymptotically flat end, we prove a density theorem which produces harmonic asymptotics on the distinguished end, while allowing for points of incompleteness (or negative scalar curvature) away from this…
The Farkas lemma is proved and applied to obtain a structure theorem for polyhedra. These notes are based on a talk in the New York Number Theory Seminar on October, 20, 2022.
We develop a new method for studying sums of Kloosterman sums related to the spectral exponential sum. As a corollary, we obtain a new proof of the estimate of Soundararajan and Young for the error term in the prime geodesic theorem.
We study compressible types in the context of (local and global) NIP. By extending a result in machine learning theory (the existence of a bound on the recursive teaching dimension), we prove density of compressible types. Using this, we…
We review some of the basic mathematical results about density functional theory.
In this paper we study an overdetermined problem which is directly related to the well known torsion problem studied by J. Serrin. A perturbed version of the latter is tackled by using asymptotic series as well as tools borrowed from the…
In this paper we solve positively the problem of (local) density of the "potentials" M(x,y) of the Moutard equation, u_{xy} = M(x,y) u, u=u(x,y), (used in many papers for construction of exact solutions of (2+1)-dimensional integrable…
In this perspective review, we present a concise yet multifaceted overview of the pivotal role played by the the shear viscosity to entropy density ratio across various physical contexts. After summarizing some of the main aspects of the…
We derive an exact equation for density changes induced by a general external field that corrects the hydrostatic approximation where the local value of the field is adsorbed into a modified chemical potential. Using linear response theory…
In this paper, as a result of a theorem of Serre on congruence properties, a complete solution is given for an open question (see the text) presented recently by Kim, Koo and Park. Some further questions and results on similar types of…
The classical isomorphism theorems for reversible Markov chains have played an important role in studying the properties of local time processes of strongly symmetric Markov processes~\cite{mr06}, bounding the cover time of a graph by a…
We prove results about uniform convergence of densities in the free central limit theorem without assumptions of boundedness on the support.
This note comments on parts of "New 5-designs." We cite Chebotarev's theorem; we correct some minor errors and we clarify our proof of the Gleason-Prange theorem.
Consider a Gaussian stationary sequence with unit variance $X=\{X_k;k\in {\mathbb{N}}\cup\{0\}\}$. Assume that the central limit theorem holds for a weighted sum of the form $V_n=n^{-1/2}\sum^{n-1}_{k=0}f(X_k)$, where $f$ designates a…
We present and prove the version of Marstrand's theorem for discrete metric space. We provide explicit estimates of the quotient of upper and lower densities of measures on this space.
We apply a new approach to the study of the density of Gabor systems, and obtain a simple and straightforward proof of Ramanathan and Steger's well known result regarding the density of Gabor frames and Gabor Riesz sequences. Moreover, this…
We explore a variety of unsolved problems in density functional theory, where mathematicians might prove useful. We give the background and context of the different problems, and why progress toward resolving them would help those doing…
We formulate and discuss a necessary and sufficient condition for polynomials to be dense in a space of continuous functions on the real line, with respect to Bernstein's weighted uniform norm. Equivalently, for a positive finite measure…