Tootfinder

On the shape of the typical Poisson-Voronoi cell in high dimensions
Matthias Irlbeck, Zakhar Kabluchko, Tobias M\"uller
https://arxiv.org/abs/2506.02607

On the shape of the typical Poisson-Voronoi cell in high dimensions
We study the typical cell of the Poisson-Voronoi tessellation. We show that when divided by the $d$-th root of the intensity parameter $λ$ of the Poisson process times the volume of the unit ball, the inradius, outradius, diameter and mean width of the typical cell converge in probability to the constants $1/2, 1, 2, 2$ respectively, as the dimension $d\to\infty$. We also show that the width of the typical cell, when rescaled in the same way, is bounded between $2\sqrt{5}/(2+\sqrt{5})-o_d(1)$ …

This https://arxiv.org/abs/2412.19480 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Inequalities between Dirichlet and Neumann Eigenvalues on Surfaces
For a bounded Lipschitz domain $Σ$ in a Riemannian surface $M$ satisfying certain curvature condition, we prove that $$μ_{3-β_1} \leq λ_{1},$$ where $μ_k$ ($λ_k$ resp.) is the $k$-th Neumann (Dirichlet resp.) Laplacian eigenvalue on $Σ$ and $β_1$ is the first Betti number of $Σ.$ If $Σ$ is smooth and simply connected, we can further derive the strict inequality $ μ_{3}< λ_{1}. $ This extends previous results on the Euclidean space to various curved surfaces, including the flat cylin…

Randomized Dimensionality Reduction for Euclidean Maximization and Diversity Measures
Jie Gao, Rajesh Jayaram, Benedikt Kolbe, Shay Sapir, Chris Schwiegelshohn, Sandeep Silwal, Erik Waingarten
https://arxiv.org/abs/2506.00165

Randomized Dimensionality Reduction for Euclidean Maximization and Diversity Measures
Randomized dimensionality reduction is a widely-used algorithmic technique for speeding up large-scale Euclidean optimization problems. In this paper, we study dimension reduction for a variety of maximization problems, including max-matching, max-spanning tree, max TSP, as well as various measures for dataset diversity. For these problems, we show that the effect of dimension reduction is intimately tied to the \emph{doubling dimension} $λ_X$ of the underlying dataset $X$ -- a quantity measur…

This https://arxiv.org/abs/2401.13116 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the second-order regularity of solutions to widely singular or degenerate elliptic equations
We consider local weak solutions to PDEs of the type \[ -\,\mathrm{div}\left((\vert Du\vert-λ)_{+}^{p-1}\frac{Du}{\vert Du\vert}\right)=f\,\,\,\,\,\,\,\text{in}\,\,Ω, \] where $1

This https://arxiv.org/abs/2404.01837 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Rotational mass of anisotropic neutron stars within Rastall gravity
Due to rotation, the mass correction of neutron stars arises and causes the rotational mass to be larger than the static mass. In this work, we extend the formulation of the rotational mass of anisotropic neutron stars within Rastall gravity. We apply numerical simulation on the formulation we obtained. We refer to mass of J0740+6620, GW170817, and GW190814 as the mass constraints of the neutron stars. For the free parameters, we use three values of Rastall's parameter, i.e. $λ=0.00019$, $λ=0…

Equidistribution and arithmetic $\Lambda$-distributions
Matthew Bertucci, Sean Howe
https://arxiv.org/abs/2505.24748 https://arxiv.or…

Equidistribution and arithmetic $Λ$-distributions
We formulate an abstract notion of equidistribution for families of $λ$-probability spaces parameterized by admissible $\mathbb{Z}$-sets. Under the assumption of equidistribution, we show that the $σ$-moment generating functions of certain infinite sums of random variables can be computed as motivic Euler products. Combining this result with earlier generalizations of Poonen's sieve, we compute the asymptotic $Λ$-distributions for several natural families of function field $L$-functions and …

This https://arxiv.org/abs/2502.10382 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On creating convexity in high dimensions
Given a subset $A$ of $\mathbb{R}^n$, we define \begin{align*} \mathrm{conv}_k(A) := \left\{ λ_1 s_1 + \cdots + λ_k s_k : λ_i \in [0,1], \sum_{i=1}^k λ_i = 1 , s_i \in A \right\} \end{align*} to be the set of vectors in $\mathbb{R}^n$ that can be written as a $k$-fold convex combination of vectors in $A$. Let $γ_n$ denote the standard Gaussian measure on $\mathbb{R}^n$. We show that for every $\varepsilon > 0$, there exists a subset $A$ of $\mathbb{R}^n$ with Gaussian measure $γ_n(A) \geq…

This https://arxiv.org/abs/2505.10439 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Interpolating Feigin-Frenkel Duality at the Critical Level to Matrices of Complex Size
In this paper, we extend Feigin-Frenkel duality at the critical level to the setting of complex rank. This is accomplished by considering the center of a vertex algebra in Deligne's interpolating categories, along with Feigin's Lie algebras of complex rank, $\mathfrak{gl}_λ$ and $\mathfrak{po}_λ$. More precisely, we define the universal affine vertex algebras associated with Lie algebras in $\underline{\mathrm{Re}}\mathrm{p}(\mathrm{GL}_α,\mathbb{F})$, $\underline{\mathrm{Re}}\mathrm{p}(\mat…

This https://arxiv.org/abs/2303.08082 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Quantum traces for $SL_n$-skein algebras
We establish the existence of several quantum trace maps. The simplest one is an algebra map between two quantizations of the algebra of regular functions on the $SL_n$-character variety of a surface $\mathfrak{S}$ equipped with an ideal triangulation $λ$. The first is the (stated) $SL_n$-skein algebra $\mathscr{S}(\mathfrak{S})$. The second $\overline{\mathcal{X}}(\mathfrak{S},λ)$ is the Fock and Goncharov's quantization of their $X$-moduli space. The quantum trace is an algebra homomorphism…

This https://arxiv.org/abs/2206.08820 has been replaced.
link: https://scholar.google.com/scholar?q=a

Resolvent estimates for the one-dimensional damped wave equation with unbounded damping
We study the generator $G$ of the one-dimensional damped wave equation with unbounded damping. We show that the norm of the corresponding resolvent operator, $\| (G - λ)^{-1} \|$, is approximately constant as $|λ| \to +\infty$ on vertical strips of bounded width contained in the closure of the left-hand side complex semi-plane, $\overline{\mathbb{C}}_{-} := \{λ\in \mathbb{C}: \operatorname{Re} λ\le 0\}$. Our proof rests on a precise asymptotic analysis of the norm of the…