Related papers: High-dimensional Sobolev tests on hyperspheres

We derive geometric formulas for the mass of asymptotically hyperbolic manifolds using coordinate horospheres. As an application, we obtain a new rigidity result of hyperbolic space: if a complete asymptotically hyperbolic manifold has…

The Sobolev regularity of invariant measures for diffusion processes is proved on non-smooth metric measure spaces with synthetic lower Ricci curvature bounds. As an application, the symmetrizability of semigroups is characterized, and the…

We propose a high dimensional mean test framework for shrinking random variables, where the underlying random variables shrink to zero as the sample size increases. By pooling observations across overlapping subsets of dimensions, we…

The Huge Object model is a distribution testing model in which we are given access to independent samples from an unknown distribution over the set of strings $\{0,1\}^n$, but are only allowed to query a few bits from the samples. We…

The asymptotic behavior of Einstein-Rosen waves at null infinity in 4 dimensions is investigated in {\it all} directions by exploiting the relation between the 4-dimensional space-time and the 3-dimensional symmetry reduction thereof.…

We discuss the asymptotic behaviour of models of lattice polygons, mainly on the square lattice. In particular, we focus on limiting area laws in the uniform perimeter ensemble where, for fixed perimeter, each polygon of a given area occurs…

Hypothesis testing in singular statistical models is often regarded as inherently problematic due to non-identifiability and degeneracy of the Fisher information. We show that the fundamental obstruction to testing in such models is not…

In this article, we study the test for independence of two random elements $X$ and $Y$ lying in an infinite dimensional space ${\cal{H}}$ (specifically, a real separable Hilbert space equipped with the inner product $\langle .,…

We prove a homogenization result for integral functionals in domains with oscillating boundaries, showing that the limit is defined on a degenerate Sobolev space. We apply this result to the description of the asymptotic behaviour of thin…

We study the nonlinear fractional reaction diffusion equation $\partial_{t}u + (-\Delta)^{s} u= f(t,x,u)$, $s\in(0,1)$ in a bounded domain $\Omega$ together with Dirichlet boundary conditions on $\R^N \setminus \Omega$. We prove asymptotic…

The effective numerical method is developed performing the test of the hyperbolicity of chaotic dynamics. The method employs ideas of algorithms for covariant Lyapunov vectors but avoids their explicit computation. The outcome is a…

We prove a monotone Sobolev extension theorem for maps to Jordan domains with rectifiable boundary in metric surfaces of locally finite Hausdorff 2-measure. This is then used to prove a uniformization result for compact metric surfaces by…

In this work we address the problem of detecting whether a sampled probability distribution of a random variable $V$ has infinite first moment. This issue is notably important when the sample results from complex numerical simulation…

In this paper we investigate the asymptotic distribution of likelihood ratio tests in models with several groups, when the number of groups converges with the dimension and sample size to infinity. We derive central limit theorems for the…

In statistics permutations typically arise in the context of rank plots for two-dimensional data. Such plots can also be interpreted as discrete copulas. In discrete mathematics, typically in the context of the description of large…

The Behrens-Fisher problem concerns testing the equality of the means of two normal populations with possibly different variances. The null hypothesis in this problem induces a statistical model for which the likelihood function may have…

In this work, we revisit the one- and two-sample testing problems: binary hypothesis testing in which one or both distributions are unknown. For the one-sample test, we provide a more streamlined proof of the asymptotic optimality of…

This paper establishes the asymptotic independence between the quadratic form and maximum of a sequence of independent random variables. Based on this theoretical result, we find the asymptotic joint distribution for the quadratic form and…

We consider an analysis of variance type problem, where the sample observations are random elements in an infinite dimensional space. This scenario covers the case, where the observations are random functions. For such a problem, we propose…

We consider classes of diffeomorphisms of Euclidean space with partial asymptotic expansions at infinity; the remainder term lies in a weighted Sobolev space whose properties at infinity fit with the desired application. We show that two…