Tootfinder

Asymptotic behavior of complete conformal metric near singular boundary
Weiming Shen, Yue Wang
https://arxiv.org/abs/2506.04591 https://

Asymptotic behavior of complete conformal metric near singular boundary
The boundary behavior of the singular Yamabe problem has been extensively studied near sufficiently smooth boundaries, while less is known about the asymptotic behavior of solutions near singular boundaries. In this paper, we study the asymptotic behaviors of solutions to the singular Yamabe problem with negative constant scalar curvature near singular boundaries and derive the optimal estimates for the background metric which is not necessarily conformally flat. In particular, we prove that th…

This https://arxiv.org/abs/2506.04091 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Mapped Exponent and Asymptotic Critical Exponent of Words
We study how much injective morphisms can increase the repetitiveness of a given word. This question has a few possible variations depending on the meaning of ``repetitiveness''. We concentrate on fractional exponents of finite words and asymptotic critical exponents of infinite words. We characterize finite words that, when mapped by injective morphisms, can have arbitrarily high fractional exponent. For infinite words, alongside other results, we show that the asymptotic critical exponent gro…

This https://arxiv.org/abs/2505.03447 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Asymptotic formula for the sum of a prime and a square-full number in intervals shorter than $X^{1/2}$
Let $R(N)$ be the number of representations of $N$ as a sum of a prime and a square-full number weighted with logarithmic function. In $2024$, the author and Y. Suzuki obtained an asymptotic formula for the sum of $R(N)$ over positive integers $N$ in a short interval ($X$, $X+H$] for $X^{\frac{1}{2}+\varepsilon} \le H < X^{1-\varepsilon}$. In this article, we improve the range of $H$, that is, we prove the same asymptotic formula for $X^{\frac{32-4\sqrt{15}}{49}+\varepsilon} \le H \le X^{1- \va…

UK National Demonstration: https://hounslowtradescouncil.org/the-peoples-assembly-national-demonstration/

The People’s Assembly National Demonstration
The People’s Assembly National Demonstration – No More Austerity 2.0 takes place on Saturday 7 June. Details are shown on the attached flyer. We are hoping that Hounslow Trades Council members will…

At the edge of Donsker's Theorem: Asymptotics of multiscale scan statistics
Johann K\"ohne, Fabian Mies
https://arxiv.org/abs/2506.05112 https://

At the edge of Donsker's Theorem: Asymptotics of multiscale scan statistics
For nonparametric inference about a function, multiscale testing procedures resolve the need for bandwidth selection and achieve asymptotically optimal detection performance against a broad range of alternatives. However, critical values strongly depend on the noise distribution, and we argue that existing methods are either statistically infeasible, or asymptotically sub-optimal. To address this methodological challenge, we show how to develop a feasible multiscale test via weak convergence ar…

Isoperimetric inequalities in Hadamard spaces of asymptotic rank two
Urs Lang, Stephan Stadler, David Urech
https://arxiv.org/abs/2506.04882 https://

Isoperimetric inequalities in Hadamard spaces of asymptotic rank two
Gromov's isoperimetric gap conjecture for Hadamard spaces states that cycles in dimensions greater than or equal to the asymptotic rank admit linear isoperimetric filling inequalities, as opposed to the inequalities of Euclidean type in lower dimensions. In the case of asymptotic rank 2, recent progress was made by Druţu-Lang-Papasoglu-Stadler who established a homotopical inequality for Lipschitz 2-spheres with exponents arbitrarily close to 1. We prove a homological inequality of the same ty…

A generalization of the ADM mass for asymptotically Euclidean manifolds of weak regularity
Stig Lundgren, Benjamin Meco
https://arxiv.org/abs/2506.02670 ht…

A generalization of the ADM mass for asymptotically Euclidean manifolds of weak regularity
We propose a new definition of the ADM mass for asymptotically Euclidean manifolds inspired by the definition of mass for weakly regular asymptotically hyperbolic manifolds by Gicquaud and Sakovich. This version of the mass allows one to work with metrics of local Sobolev regularity $ W^{1,2}_\text{loc} \cap L^\infty $ and we show, under suitable asymptotic assumptions, that the mass is finite, invariant under a change of coordinates at infinity and that it agrees with the classical ADM mass in…

This https://arxiv.org/abs/2505.01874 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Towards Trustworthy Federated Learning with Untrusted Participants
Resilience against malicious participants and data privacy are essential for trustworthy federated learning, yet achieving both with good utility typically requires the strong assumption of a trusted central server. This paper shows that a significantly weaker assumption suffices: each pair of participants shares a randomness seed unknown to others. In a setting where malicious participants may collude with an untrusted server, we propose CafCor, an algorithm that integrates robust gradient agg…

Classification of the real Painlev\'{e} I transcendents by zeros and connection problem: an asymptotic study
Yan Huang, Yu-Tian Li, Wen-Gao Long
https://arxiv.org/abs/2506.03648

Classification of the real Painlevé I transcendents by zeros and connection problem: an asymptotic study
In this paper, we study the asymptotic behavior and connection problem of Painlevé I (PI) equation through a detailed analysis of the Stokes multipliers associated with its solutions. Focusing on the regime where the derivative at the real zeros of the solution becomes large, we apply the complex WKB method to derive full asymptotic expansions of the Stokes multipliers. These expansions allow us to classify real solutions of PI according to their behavior at the zeros, distinguishing between o…

This https://arxiv.org/abs/2505.03447 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Asymptotic formula for the sum of a prime and a square-full number in intervals shorter than $X^{1/2}$
Let $R(N)$ be the number of representations of $N$ as a sum of a prime and a square-full number weighted with logarithmic function. In $2024$, the author and Y. Suzuki obtained an asymptotic formula for the sum of $R(N)$ over positive integers $N$ in a short interval ($X$, $X+H$] for $X^{\frac{1}{2}+\varepsilon} \le H < X^{1-\varepsilon}$. In this article, we improve the range of $H$, that is, we prove the same asymptotic formula for $X^{\frac{32-4\sqrt{15}}{49}+\varepsilon} \le H \le X^{1- \va…