arXiv preprints from January 1, 2026 through July 21, 2026 — 06:04:33 EST
There exist conformally invariant, higher-derivative, variational analogs of the Yang-Mills condition for connections on vector bundles over a conformal manifold of even dimension greater than or equal to six. We give a compact formula for these analogs and prove that they are a strict weakening of the Yang-Mills condition with...
We develop an operator-theoretic formulation of stochastic calculus for fractional Brownian motion with Hurst parameter H in (0, 1/2). The approach is based on adjointness between stochastic integration and differentiation in the Cameron-Martin space of the driving process. For Gaussian Volterra processes, we establish a canonical...
Let Y be a random variable satisfying specific moment conditions. This paper introduces and investigates probabilistic heterogeneous Stirling numbers of the second kind and probabilistic heterogeneous Bell polynomials. These structures unify several classical and probabilistic families, including those of Stirling, Lah, Bell and...
Let $G$ be an infinite, connected, locally finite planar graph and consider i.i.d.\ Bernoulli$(p)$ site percolation. Write $p_c^{\mathrm{site}}(G)$ and $p_u^{\mathrm{site}}(G)$ for the critical and uniqueness thresholds. Using a well--separated Freudenthal embedding $G\hookrightarrow\mathbb S^2$, we introduce a cycle--separation...
Let $C$ be a smooth projective curve over an algebraically closed field ${\mathbb{F}}$ equipped with the action of a finite group $G$. When $p =\textrm{char}(\mathbb{F})$ divides the order of $G$, the long-standing problem of computing the induced representation of $G$ on the space $H^0(C,Ω^{\otimes m}_C)$ of globally holomorphic...
In this paper, we construct directed strongly regular graphs and divisible design graphs with new parameters merging some basic relations of so-called Tatra associations schemes. We also study the above association schemes, their fusions and isomorphisms.
For Bernoulli site percolation on an infinite, connected, locally finite graph $G=(V,E)$, we obtain quantitative upper bounds on the supercritical disconnection probability \[ \mathbb{P}_p(S\nleftrightarrow\infty) \] for arbitrary finite or infinite sets $S\subset V$ and all $p>p^{\mathrm{site}}_c(G)$. The key quantity is a...
The choice of the tuning parameter in the Lasso is central to its statistical performance in high-dimensional linear regression. In this work, we study tuning regimes under which the Lasso exhibits suboptimal prediction performance, in the sense that a simple refinement improves upon it both on high-probability events and in mean...
In this paper, we propose a novel reformulation of the smooth nonconvex-strongly-concave (NC-SC) minimax problems that casts the problem as a joint minimization. We show that our reformulation preserves not only first-order stationarity, but also global and local optimality, second-order stationarity, and the Kurdyka-Łojasiewicz (KL)...
In this paper we obtain several results related to the $p$-adic interpolation of the classical Cogdell lift, mapping special cycles on Picard modular surfaces to elliptic modular forms. The results have a three-fold nature: in the first part of the paper, we $p$-adically interpolate the adjoint Kudla lift, exploiting the previously...
We establish sharp rates for propagation of chaos in Rényi divergences for interacting diffusion systems at stationarity. Building upon the entropic hierarchy established in Lacker (2023), we show that under strong isoperimetry and weak interaction conditions, one can achieve $\mathsf R_q(μ^1 \,\lVert\, π) = \widetilde O(\frac{d...
For $d\geq 4$, Kalai (1987) characterized all simplicial $(d-1)$-spheres with $g_2=0$, and for $k\geq 2$ and $d\geq 2k$, Murai and Nevo (2013) characterized all simplicial $(d-1)$-spheres with $g_k=0$. In addition, for $d\geq 4$, Nevo and Novinsky (2011) characterized all simplicial $(d-1)$-spheres with $g_2=1$. Motivated by these...
In this paper, we develop a general theory for the transport equation within the framework of Triebel-Lizorkin spaces. We first derive commutator estimates in these spaces, dispensing with the conventional divergence-free condition, via the Bony paraproduct decomposition and vector-valued maximal function inequalities. Building on...
We study the subgradient method for factorized robust signal recovery problems, including robust PCA, robust phase retrieval, and robust matrix sensing. The resulting objectives are nonsmooth and nonconvex, and can have unbounded sublevel sets, so standard analyses based on descent and coercivity do not apply. For locally Lipschitz...
We present a fast, unconditionally energy-stable numerical scheme for simulating vesicle deformation under osmotic pressure using a phase-field approach. The model couples an Allen-Cahn equation for the biomembrane interface with a variable-mobility Cahn-Hilliard equation governing mass exchange across the membrane. Classical...
We prove Kovács' conjecture that claims that if the $p^{th}$ exterior power of the tangent bundle of a smooth complex projective variety contains the $p^{th}$ exterior power of an ample vector bundle then the variety is either projective space or the $p$-dimensional quadric hypersurface. We also prove a similar characterization...
Based on M. Hall's theorem we prove a simple result dealing with real numbers which admit exact approximations by rationals.
For $a,b,c,z,p, θ\in \mathbb{C}$, where $\mathbb{C}$ is the complex plane, $-c\notin \mathbb{N\cup }\left\{ 0\right\} $, let \begin{equation*} \mathcal{M}\left( z\right) =\left( 1-θz\right) ^{p}M\left(a;c;z\right) =\sum_{n=0}^{\infty }u_{n}z^{n}, \end{equation*} where $|z| <\frac{1}θ$, $|\arg (1-θz)| < π$, and let \begin{equation*}...
For a graph $G$, let $λ_1(G)$ and $λ_2(G)$ denote the largest and the second largest adjacency eigenvalue of $G$. The sum $λ_1(G) + λ_2(G)$ is called the \emph{spectral sum} of $G$. We investigate the spectral sum of trees of order $n$ and determine the extremal trees that achieve maximum/minimum. Moreover, for any $α\in [0,1]$, we...
The aim of this article is to prove that the linear stability or instability of small Bernstein-Green-Kruskal (BGK) waves is determined by the sign of the derivative of their energy distributions at $0$ energy.
In this paper, we introduce a Ketonen-type Gentzen-style classical simple type theory $\bf KCT$. Also the tableau system $\bf KCTT$ corresponding to $\bf KCT$ is introduced. Further inference-preserving Gentzen system $\bf KCT_h$ (equivalent to $\bf KCT$) and tableau system $\bf KCTT_h$ (equivalent to $\bf KCTT$) is introduced. We...
This article is based on a talk given at the Ghent Geometric Analysis Seminar in 2023. We review basic notions from the theory of weightings along submanifolds, with special emphasis on multiplicative weightings for Lie groupoids along subgroupoids.
In this paper, we concern with the Sasaki analogue of Yau uniformization conjecture in a complete noncompact Sasakian manifold with nonnegative transverse bisectional curvature. As a consequence, we confirm that any $5$-dimensional complete noncompact Sasakian manifold with positive transverse bisectional curvature and the maximal...
We discuss and draw the reader's attention to several passages in Vladimir Arnold's note on the epigraph to the novel in verse "Evgenii Onegin" by A$.$S$.$Pushkin, as well as to puzzles hidden in the novel by the poet himself.
Our objective is to illuminate the global structure of non-orientable manifolds with signature-changing metrics, with particular emphasis on global topological obstructions. Using explicit geometric constructions based on the topology of the Möbius strip, we produce examples of crosscap manifolds where the gluing junction coincides...