arXiv preprints from January 1, 2026 through September 6, 2026 — 23:48:03 EST
In this paper we study maximal and oscillation inequalities for multi-parameter discrete Radon averaging operators. We develop a robust variant of the multi-parameter circle method within the framework of Discrete Analogues in Harmonic Analysis. In particular, this gives quantitative estimates for these averages and their underlying...
We adapt the classical topological notions of properly discontinuous group actions to the framework of coarse geometry. By substituting the rigid constraints of local compactness and discreteness with uniform coarse equivalences, we systematically resolve the topological obstructions identified by Kapovich. We establish comprehensive...
Given a degree sequence $d$, the realization graph $\mathcal{G_F}(d)$ is the graph whose vertices are all labeled realizations of $d$, where two realizations are adjacent if they differ by a single $2$-switch. We prove that $\mathcal{G_F}(d)$ admits a Hamilton path for every degree sequence $d$. The problem was initiated by Arikati...
We give a definition of coverings and branched coverings on general (non-locally connected) metric spaces and study their lifting properties. Instead of lifting curves the theory is developed by lifting continua. An alternative homotopy theory is depicted and versions generalizing the classical results are given. We study applications...
Dengue remains a major public health challenge in tropical regions, and recurring outbreaks suggest that current intervention strategies are not yet fully effective. Existing mathematical models typically assume unlimited hospital capacity and continuously applied fogging, neglecting practical constraints that strongly influence...
We use the tropical trigonal construction to describe the minimal toroidal resolution of the Prym period map $\overline{R}_4\dashrightarrow\overline{A}_3$.
We consider a novel robust utility maximisation problem under bounded cumulative transition rate uncertainty within the class of non-Markovian marked point processes on a finite state-space. Utility is maximised over the class of admissible controls, while Nature chooses a worst-case biometric scenario from the class of admissible,...
Let $V$ be an $n$-dimensional Euclidean vector space, ,where $n\ge 4$, and $\ell = \lfloor\frac{n}{2}\rfloor$. We prove the sharp pointwise estimate \[ q_2(E) \ge -\frac{2(\ell -1)}{3\ell} \mathrm{Scal}(E) \mathrm{Id}_{Λ^2V^*} \] for every algebraic curvature tensor $E$ on $V$ with nonnegative sectional curvature. Applying...
We investigate entropy production and nonequilibrium transport in a class of random dynamical systems modeling a Knudsen gas confined to a compartmented container. The system consists of a single particle undergoing random billiard motion, with collisions leading to random reflection or transmission through semi-reflecting,...
Disordered systems such as spin glasses and polymers characteristically exhibit random energy landscapes with many macroscopically separated energetic valleys corresponding to near-ground states. This high complexity renders these systems extremely sensitive to perturbations of external parameters. For instance, the support of...
This paper considers a multi-environment factor model in which high-dimensional covariates are collected from heterogeneous environments, with auxiliary labels available in a subset of these environments. The joint distribution of the covariates may vary across environments, whereas the latent structure is decomposed into invariant...
We investigate the combinatorial structure of the tropical characteristic polynomial of symmetric matrices using the tropical permanents of their principal submatrices. We establish new inequalities for the leading coefficients of the tropical characteristic polynomial, revealing concavity properties of the coefficient sequence and...
We give a complete characterization of the (purely infinite) simplicity of Katsura algebras and the associated Steinberg algebras. This is achieved by characterizing when the singular ideals vanish via the self-similar groupoid model derived from Exel and Pardo. Analogous results are given for the algebras arising from the faithful...
We consider the space of $(n-1)$-colored graphs on a fixed set of $N$ vertices. Each edge position of the complete graph $K_N$ has $n$ possible states: the absence of an edge and $n-1$ colors. This gives a natural identification of the space of such graphs with the tensor power $(\mathbb C^n)^{\otimes m}$, where $m=\binom N2$, and...
A new approach for nonparametric estimation of the quantile density function (sparsity function) and its derivatives is suggested which is based on local polynomial estimation. The estimator has more advantageous properties at the boundaries than classical quantile density estimators. Asymptotic normality is shown and the bias,...
Self-distillation (SD) is typically studied when the student is retrained on the teacher's original training inputs. In many practical deployments, however, the labeled training data are no longer available, and one has access only to the trained predictor and fresh unlabeled covariates. We study SD in this prediction-only regime...
Bacterial chemotactic movement and collective aggregation have long attracted substantial interest in mathematical biology and applied modeling. Classical Keller--Segel-type systems, however, are typically formulated under idealized laboratory assumptions, such as smooth agar substrates, and thus cannot adequately capture the gliding...
Let $Ω(n)$ denote the number of prime factors of $n$, counted with multiplicity, and put $P_2$={$m$ $\ge$ 1:$Ω(m)$ $\le$ 2}. We prove that the sumset $P_2$+{$a^a$: a$\ge$ 1} has positive lower density. The proof uses the Romanoff second moment method, in the spirit of Li and Pan's theorem on $P_2$+$2^{\mathcal P}$. The main new...
In this paper, we investigate the compositional inverses of permutation polynomials of the form \[ F(x)=h(ψ(x))\varphi(x)+g(ψ(x)) \in \mathbb{F}_{q^n}[x], \] where \(ψ(x),\varphi(x) \in \mathbb{F}_{q^n}[x]\) are additive polynomials, \(h(x), g(x) \in \mathbb{F}_{q^n}[x]\) satisfy $ h(ψ(\mathbb{F}_{q^n})) \subseteq...
For $r\geq 3$ we denote by $\mathcal{C}(D_r)$ the Cartan matrix of type $D_r$. Recently, Sun and Wang conjectured a Rogers--Ramanujan type identity for the Nahm sum associated with $\mathcal{C}(D_r)^{-1}$ and the zero vector. They further conjecture that there exist $r-1$ companion modular Nahm sums associated with nonzero vectors. We...
Classes of graphs excluding a path and a biclique as induced subgraphs are extensively studied in the literature. One of the key structural results for such graphs is a Ramsey-type result due to Galvin, Rival, and Sands (1982), establishing the existence of a function $f$ bounding the maximum length of a path in terms of clique number...
We prove that the only planar, centrally symmetric, strictly convex body $K\subset\mathbb{R}^2$ with $C^1$ boundary that floats in equilibrium in every orientation for the perimetral densities $σ=\tfrac18$ or $σ=\tfrac38$ is a disk.
Let $\emph{spex}_{\mathcal{P}}(n,F)$ and $\emph{spex}_{\mathcal{OP}}(n,F)$ be the maximum spectral radius among all $n$-vertex $F$-free planar graphs and outerplanar graphs, respectively. Define $C_{k,l}$ as a graph obtained from $C_k \cup C_l$ such that the two cycles share a common vertex, where $l \ge k \ge 3$. In the 1990s,...
The class of $q$-Bass martingales provides a natural answer to a central question in martingale optimal transport: how to construct martingales with prescribed initial and terminal marginals whose transition kernel remains as close as possible to a given reference measure $q$. We prove the existence of $q$-Bass martingales when the...
We propose a definition of the reduction type of a curve over a discretely valued field in terms of the special fibre of an arbitrary regular model. We show that under this definition, the reduction type in terms of the minimal regular model determines and reduction type in terms of the minimal regular normal crossings model and vice...