arXiv research

We define the (total) center of mass for suitably asymptotically hyperbolic time-slices of asymptotically anti-de Sitter spacetimes in general relativity. We do so in analogy to the picture that has been consolidated for the (total) center of mass of suitably asymptotically Euclidean time-slices of asymptotically Minko…

The asymptotic lattices and their transformations are studied within the line geometry approach. It is shown that the discrete asymptotic nets are represented by isotropic congruences in the Plucker quadric. On the basis of the Lelieuvre-type representation of asymptotic lattices and of the discrete analog of the Mouta…

Novel approach for large genus intersection number asymptotics.

Asymptotic behavior of energy of a harmonic map defined on an asymptotically hyperbolic manifold is considered. Using the growth of energy, we show that a harmonic map defined on some asymptotically hyperbolic manifolds has to be constant if the total energy is finite, or if the map approaches a point fast enough, in t…

This paper is devoted to dualization of dimension-theoretical results from the small scale to the large scale. So far there are two approaches for such dualization: one consisting of creating analogs of small scale concepts and the other amounting to the covering dimension of the Higson corona $ν(X)$ of $X$. The first …

We introduce the notion of asymptotic cohomology based on the bounded cohomology and define cohomological asymptotic dimension $\as_{\Z} X$ of metric spaces. We show that it agrees with the asymptotic dimension $\as X$ when the later is finite. Then we use this fact to construct an example of a metric space $X$ of boun…

Unified definition of mass aspect function for weakly regular hyperbolic manifolds.

Study finds necessary conditions for black hole geometries to asymptotically approach Kerr-de Sitter spacetime.

Researchers extend asymptotic analysis to Bergman projections with Gevrey weights.

Study geometric characterization of asymptotic pseudodifferential calculus on spinor bundles.

We show that the mass of an asymptotically hyperbolic manifold with a noncompact boundary can be evaluated via the Ricci tensor and the second fundamental form by using purely coordinates. The method is analog to Miao-Tam's approach to the asymptotically flat manifold.

Study on eigenvalue rate of geodesic balls in asymptotically hyperbolic Einstein manifolds.

This paper analyzes the distribution of genera in 2-bridge knots and proves their asymptotic normality.

In this paper, based on an intrinsic definition of asymptotically AdS space-times, we show that the standard anti-de Sitter space-time is the unique strictly stationary asymptotically AdS solution to the vacuum Einstein equations with negative cosmological constant in dimension less than 7. Instead of using the positiv…

In this paper, using the Greiner's approach to heat kernel asymptotics, we give new proofs of the equivariant Gauss-Bonnet-Chern formula and the variation formulas for the equivariant Ray-Singer metric, which are originally due to J. M. Bismut and W. Zhang.

We develop a local theory for the construction of singular spacetimes in all spacetime dimensions which become asymptotically self-similar as the singularity is approached. The techniques developed also allow us to construct and classify exact self-similar solutions which correspond to the formal asymptotic expansions …

Although consistency is a minimum requirement of any estimator, little is known about consistency of the mean partition approach in consensus clustering. This contribution studies the asymptotic behavior of mean partitions. We show that under normal assumptions, the mean partition approach is consistent and asymptotic …

Study tail behavior of sum of heavy-tailed risks with copulas.

This paper improves offline contextual bandits using distributional robustness.

Study refracted skew Brownian motion, find densities and asymptotics.

Improved control approach for correlated bandits with better performance.

Solves asymptotic $A_n$-realization problem for curves.

Paper explores weighted averaging schemes for SGD, achieving asymptotic normality and optimality.

Optimizes MCMC chains with neural control variates.

Study asymptotic behavior of translators in hyperbolic product space.

Estimates growth of reciprocal classes in Hecke groups.

The paper studies reward concentration in MDPs, covering asymptotic and non-asymptotic settings.

Optimizes stochastic linear bandits with efficient, asymptotically optimal algorithm.

Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether solutions have finite extent (stars with a vacuum exterior) or infinite extent. In the l…

In this note, we propose an approach to the study of the analogue for unipotent harmonic bundles of Schmid's Nilpotent Orbit Theorem. Using this approach, we construct harmonic metrics on unipotent bundles over quasi-compact Kähler manifolds with carefully controlled asymptotics near the compactifying divisor; such a m…

A framework to compare federated learning algorithms in high-dimensional settings.

The paper analyzes stability and asymptotic behavior of hedging strategies in binomial and trinomial models.

Researchers use conformal infinity to study spacetimes near AdS2×S2.

Uniformly K-stable toric varieties are asymptotically Chow stable if their Futaki-Ono invariant vanishes.

Study fractional perimeter asymptotics on Riemannian manifolds as $s$ approaches 0.

In this paper we study the small time asymptotics for the heat kernel on a sub-Riemannian manifold, using a perturbative approach. We then explicitly compute, in the case of a 3D contact structure, the first two coefficients of the small time asymptotics expansion of the heat kernel on the diagonal, expressing them in …

We prove a positive mass theorem for spaces which asymptotically approach a flat Euclidean space times a Calabi-Yau manifold (or any special honolomy manifold except the quaternionic Kähler). This is motivated by the very recent work of Hertog-Horowitz-Maeda.

This paper considers magnitude, asymptotics and duration of drawdowns for some Lévy processes. First, we revisit some existing results on the magnitude of drawdowns for spectrally negative Lévy processes using an approximation approach. For any spectrally negative Lévy process whose scale functions are well-behaved at …

We follow the approach employed by Y. Choquet-Bruhat, J. Isenberg and D. Pollack in the case of closed manifolds and establish existence and non-existence results for the Einstein-scalar field constraint equations on asymptotically hyperbolic manifolds.

Paper constructs solutions to Bogomolny equations with specific boundary and asymptotic conditions.

Novel approach to wave equations near null infinity in flat spacetimes.

Researchers prove a Penrose inequality for spacetime with specific conditions.

Develops a new model-free approach to portfolio theory using rough paths.

Unified asymptotics for investment in markets with transaction costs and search frictions.

Study analyzes low-energy behavior of Schrödinger operators with Coulomb potentials.

Asymptotic cones of metric spaces were first invented by Gromov. They are metric spaces which capture the 'large-scale structure' of the underlying metric space. Later, van den Dries and Wilkie gave a more general construction of asymptotic cones using ultrapowers. Certain facts about asymptotic cones, like the complet…

In this work we obtain the limit of the Hawking energy of a large class of foliations along general null hypersurfaces $Ω$ satisfying a weak notion of asymptotic flatness. The foliations are not required to be either geodesic or approaching large spheres at infinity. The limit is obtained in terms of a reference backgr…

Sharp criterion for Chern-Gauss-Bonnet integral using Q curvature.