Related papers: Addendum: EPRL/FK Asymptotics and the Flatness Pro…
We revisit and adapt the extended sequential quadratic method (ESQM) in [3] for solving a class of difference-of-convex optimization problems whose constraints are defined as the intersection of level sets of Lipschitz differentiable…
Bennett, Carbery and Tao considered the $k$-linear restriction estimate in $\mathbb{R}^{n+1}$ and established the near optimal $L^\frac2{k-1}$ estimate under transversality assumptions only. We have shown that the trilinear restriction…
Expectation Propagation is a very popular algorithm for variational inference, but comes with few theoretical guarantees. In this article, we prove that the approximation errors made by EP can be bounded. Our bounds have an asymptotic…
Let $g$ be a metric on the $2$-sphere $\mathbb{S}^2$ with positive Gaussian curvature and $H$ be a positive constant. Under suitable conditions on $(g, H)$, we construct smooth, asymptotically flat $3$-manifolds $M$ with non-negative scalar…
We prove an extension of the Regularity Lemma with vertex and edge weights which can be applied for a large class of graphs. The applications involve random graphs and a weighted version of the Erd\H{o}s-Stone theorem. We also provide means…
Classical Edgeworth expansions provide asymptotic correction terms to the Central Limit Theorem (CLT) up to an order that depends on the number of moments available. In this paper, we provide subsequent correction terms beyond those given…
The physics of complex systems stands to greatly benefit from the qualitative changes in data availability and advances in data-driven computational methods. Many of these systems can be represented by interacting degrees of freedom on…
A refinement of Bennett's inequality is introduced which is strictly tighter than the classical bound. The new bound establishes the convergence of the average of independent random variables to its expected value. It also carefully…
We obtain exact formulas for moments and generating functions of the height function of the asymmetric simple exclusion process at one spatial point, starting from special initial data in which every positive even site is initially…
We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…
We extend the idea and techniques in \cite{Miao} to study variational effect of the boundary geometry on the ADM mass of an asymptotically flat manifold. We show that, for a Lipschitz asymptotically flat metric extension of a bounded…
We analyze the question of possible quantum corrections in the entropic scenario of emergent gravity. Using a fuzzy sphere as a natural quasiclassical approximation for the spherical holographic screen, we analyze whether it is possible to…
We derive a number of sharp upper bounds for the deficit in the Alexandrov-Fenchel inequality using a weighted Minkowski integral formula and an integral formula for the deficit in Jensen's inequality. Our estimates yield results under…
Inspired by Goette-Semmelmann \cite{GSSU2002}, we derive an estimate for the scalar curvature without a nonnegativity assumption on curvature operator. As an application, we show that, on an even dimensional closed manifold with nonzero…
We obtain a priori local pointwise second derivative estimates for solutions $u$ to a class of augmented Hessian equations on Riemannian manifolds, in terms of the $C^1$ norm and certain $W^{2,p}$ norms of $u$. We consider the case that no…
In this article we give explicit formulae for a lift of the relative Frobenius morphism between elliptic curves and show how one can compute this lift in the case of ordinary reduction in odd characteristic. Our theory can also be used in…
Kossowski and Kriele derived boundary conditions on the metric at a surface of signature change. We point out that their derivation is based not only on certain smoothness assumptions but also on a postulated form of the Einstein field…
It was shown long ago by T. V. Ruzmaikina and A. A. Ruzmaikin that within the framework of a homogeneous and isotropic cosmological model quadratic corrections of the gravitational field cannot provide solutions that are both regular…
The current paper introduces classical, relativistic Lagrangians for point-particle analogs to the field theory description of the Standard-Model Extension (SME) for Lorentz violation. Lagrangians of a form alternative to those derived and…
The aim of the paper is to address the behavior in large population of diffusions interacting on a random, possibly diluted and inhomogeneous graph. This is the natural continuation of a previous work, where the homogeneous Erd\H os-R\'enyi…