arXiv research

Proves positive mass theorem for 3-manifolds with a boundary.

Proves smoothness of conical singularities in mean curvature flow.

Study on Chern-Simons theory at generic levels, revealing universal resurgent structure.

We show that at the level of formal expansions, any compact Riemannian manifold is the sphere at infinity of an asymptotically conical gradient expanding Ricci soliton.

Researchers prove a Penrose inequality for spacetime with specific conditions.

Study equi-affine invariants for convex domains with asymptotes.

Estimates population mean from user-level data with privacy, accounting for heterogeneity.

We consider a data corruption scenario in the classical $k$ Nearest Neighbors ($k$-NN) algorithm, that is, the testing data are randomly perturbed. Under such a scenario, the impact of corruption level on the asymptotic regret is carefully characterized. In particular, our theoretical analysis reveals a phase transitio…

Paper examines risk measure expansions under FGM dependence, improving accuracy at extreme levels.

The paper constructs hypersurfaces translating under powers of Gauss curvature.

Develops privacy-preserving methods for longitudinal linear regression.

Proves mean curvature flow from conical singularities to shrinkers.

New algorithm reduces sample complexity for Top Two method.

We study the asymptotic behaviour of 1-parameter subgroups with respect to Hofer's metric when the underlying symplectic manifold is an open surface of infinite area. We prove that, depending on the topology of the level sets of the Hamiltonian H, the distance either is bounded or behaves asymptotically linear. Moreove…

We study an optimal investment control problem for an insurance company. The surplus process follows the Cramer-Lundberg process with perturbation of a Brownian motion. The company can invest its surplus into a risk free asset and a Black-Scholes risky asset. The optimization objective is to minimize the probability of…

We study the asymptotic behavior of convex Cauchy hypersurfaces on maximal globally hyperbolic spatially compact space-times of constant curvature. We generalise the result of [11] to the (2+1) de Sitter and anti de Sitter cases. We prove that in these cases the level sets of quasi-concave times converge in the Gromov …

We study the asymptotic behaviour of the quantum representations of the modular group in the large level limit. We prove that each element of the modular group acts as a Fourier integral operator. This provides a link between the classical and quantum Chern-Simons theories for the torus. From this result we deduce the …

The paper studies eigenvalues in gaps of the essential spectrum of a Bochner-Schrödinger operator.

The paper addresses the gap between theoretical and practical confidence set widths in universal inference.

We characterize the asymptotic performance of nonparametric one- and two-sample testing. The exponential decay rate or error exponent of the type-II error probability is used as the asymptotic performance metric, and an optimal test achieves the maximum rate subject to a constant level constraint on the type-I error pr…

We study the asymptotic behavior of the difference $Δρ^{X, Y}_α:= ρ_α(X + Y) - ρ_α(X)$ as $α\rightarrow 1$, where $ρ_α$ is a risk measure equipped with a confidence level parameter $0 < α< 1$, and where $X$ and $Y$ are non-negative random variables whose tail probability functions are regularly varying. The case where …

Researchers compute trace formula for magnetic Laplacian on hyperbolic surfaces.

Game theory model shows optimal investment strategy for wealth growth.

This paper presents the first theoretical results showing that stable identification of overcomplete $μ$-coherent dictionaries $Φ\in \mathbb{R}^{d\times K}$ is locally possible from training signals with sparsity levels $S$ up to the order $O(μ^{-2})$ and signal to noise ratios up to $O(\sqrt{d})$. In particular the di…

New asymptotic e-values improve inference by eliminating data-dependent scaling inefficiency.

Consider the Chern-Simons topological quantum field theory with gauge group SU(2) and level k. Given a knot in the 3-sphere, this theory associates to the knot exterior an element in a vector space. We call this vector the knot state and study its asymptotic properties when the level is large. The latter vector space b…

We characterize the asymptotic performance of nonparametric goodness of fit testing. The exponential decay rate of the type-II error probability is used as the asymptotic performance metric, and a test is optimal if it achieves the maximum rate subject to a constant level constraint on the type-I error probability. We …

New flexible confidence sequences for robust statistical inference.

We derive formulas for the Reshetikhin-Turaev invariants of all oriented Seifert manifolds associated to an arbitrary complex finite dimensional simple Lie algebra $\mathfrak g$ in terms of the Seifert invariants and standard data for $\mathfrak g$. A main corollary is a determination of the full asymptotic expansions …

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…

Paper introduces new estimator for continuous treatment effects.

Study resolves conjecture on overparameterized linear models' generalization.

The goal of this paper is to measure the non-convexity of compact and smooth connected components of real algebraic plane curves. We study these curves first in a general setting and then in an asymptotic one. In particular, we consider sufficiently small levels of a real bivariate polynomial in a small enough neighbou…

We analyze the level sets of the norm of the Witten spinor in an asymptotically flat Riemannian spin manifold of positive scalar curvature. Level sets of small area are constructed. We prove curvature estimates which quantify that, if the total mass becomes small, the manifold becomes flat with the exception of a set o…

Improved MLMC method boosts risk estimation efficiency.

A new algorithm estimates mean under varying user data sizes with local differential privacy.

Paper improves risk estimation for extreme events.

New proof of Penrose inequality using potential theory.

The study finds a trade-off between model size, test loss, and training loss for linear predictors.

New bounds on efficiency for conformalized regression methods.

New methods using spacetime harmonic functions solve geometric inequalities.

Optimal convex loss function improves regression coefficient estimation.

Correlation mixtures of elliptical copulas arise when the correlation parameter is driven itself by a latent random process. For such copulas, both penultimate and asymptotic tail dependence are much larger than for ordinary elliptical copulas with the same unconditional correlation. Furthermore, for Gaussian and Stude…

Study bounds noise level in linear regression with dependent data.

Using geometric quantization, we represent curve operators in the TQFT of Witten-Reshetikhin-Turaev with jauge group SU_2 as Toeplitz operators with symbols corresponding to trace functions. As an application, we show that eigenvectors of these operators are concentrated near the level sets of these trace functions, an…

Semiparametric method removes bias in functional bilevel gradient estimation.

This paper shows how to combine optimal tests into log-optimal processes.

We establish various results on the large level limit of projective quantum representations of surface mapping class groups obtained by quantizing moduli spaces of flat SU(n)-bundle. Working with the metaplectic correction, we proved that these projective representations lift to asymptotic representations. We show that…