arXiv preprints from January 1, 2026 through September 22, 2026 — 01:56:12 EST
We establish a comparison principle for viscosity solutions of a class of nonlinear partial differential equations posed on the space of nonnegative finite measures, thereby extending recent results for PDEs defined on the Wasserstein space of probability measures. As an application, we study a controlled branching McKean-Vlasov...
The well-known Zalcman conjecture, which implies the Bieberbach conjecture, states that the coefficients of univalent functions $f(z) = z + \sum\limits_2^{\infty} a_n z^n$ on the unit disk satisfy $|a_n^2 - a_{2n-1}| \le (n-1)^2$ for all $n > 2$, with equality only for the Koebe function and its rotations. The conjecture was proved by...
Let $R$ be a finite local ring. We prove a quantitative universality statement for the cokernel of random matrices with i.i.d. entries valued in $R$. Rather than use the moment method, we use the Lindeberg replacement technique. This approach also yields a universality result for several invariants that are finer than the cokernel,...
We deform block triangular Jacobi matrices appearing in geometry, look at multi-scale Barycentric limits of geometries and droplet boundary manifolds in Potts networks.
We provide a one-parameter family of Lorentz-Riemann signature-change models of metric manifolds. This family generalizes the Kossowski's signature type-changihg stablished in [9]. Simple local expressions are sought around the hypersurface of change.
We disprove the natural domain extension of the Berger--Coburn heat-flow conjecture for Toeplitz operators on the Bargmann space and identify the failure mechanism as a gap between pointwise and uniform control of a Gaussian averaging of the squared modulus of the symbol, a gap that is invisible to the linear form $T_g$. We establish...
This paper describes the vector bundle on the elliptic modular curve that is associated to a vertex operator algebra $V$ (VOA) or more generally a quasi-vertex operator algebra (QVOA), with a view towards future applications aimed at studying the characters of VOAs. We explain how the modes of sections of $V$ give rise naturally to...
Let $\mathfrak{o}$ be the ring of integers of a non-archimedean local field with residue field of odd characteristic, $\mathfrak{p}$ be its maximal ideal and let $\mathfrak{o}_\ell = \mathfrak{o}/\mathfrak{p}^\ell$ for $\ell\ge 2$. In this article, we study real-valued characters and real representations of the finite groups...
Spectral interference, the frequency counterpart of the beating phenomenon in the time domain, can severely distort time-frequency representations (TFRs) in physical applications. We study this phenomenon for the short-time Fourier transform (STFT) with a Gaussian window and for nonlinear refinements based on the reassignment method,...
We introduce the notion of a Nachbin proximity on a bounded archimedean $\ell$-algebra (bal-algebra), and show that Gelfand duality lifts to yield a dual equivalence between the category of uniformly complete bal-algebras equipped with a closed Nachbin proximity and that of Nachbin spaces (compact ordered spaces). The key ingredients...
Many real-world dynamics exhibit chaos, a phenomenon in which neighboring trajectories in the state space of a dynamical system diverge exponentially over time. A common measure used for quantifying the degree of this divergence is the maximal Lyapunov exponent, which relies on pairwise Euclidean distances between the trajectories at...
In this paper, we give a uniform upper bound on the rational points of bounded height provided by conics in a cubic surface. For this target, we give a generalized version of the global determinant method of Salberger by Arakelov geometry.
Recently, in the context of walks of hexagonal circle packings, interest has emerged in the family of skew Dyck paths with two variants of down-steps. These paths have steps $U, D_g, D_b, L=D_r$. Using generating functions, the kernel method and (in)finite linear systems, contributions to the (average) height and other enumerations...
The recently established spectral Favard theorem for bounded banded matrices admitting a positive bidiagonal factorization is applied to a broader class of Markov chains with bounded banded transition matrices, extending beyond the classical birth-and-death setting, to those that allow a positive stochastic bidiagonal factorization....
The cross-ratio degree problem asks for the number of configurations of $n$ points in $\mathbb{P}^1$ that satisfy $n-3$ specified cross-ratio conditions. It is known that the maximal cross-ratio degree for 8 points is at least 4. In this paper, we will see that the maximal cross-ratio degree for 8 points in $\mathbb{P}^1$ is equal to 4.
We propose a structure-preserving scheme for a hybrid model that couples the time-dependent Ginzburg-Landau (TDGL) equation of superconducting vortex dynamics and the nonlinear Bardeen-Cooper-Schrieffer (BCS) gap equation. This formulation is consistent with the classical TDGL equation in the near-critical temperature, while extending...
We construct a group associated to a class of Borcherds algebras that admit a direct sum decomposition into a Kac--Moody (or semi-simple) subalgebra and a pair of free Lie subalgebras. Such Borcherds algebras have no mutually orthogonal imaginary simple roots.Our group is a semi-direct product of a Kac--Moody (or semi-simple) group...
We consider a family $\{(u_\varepsilon, v_\varepsilon)\}_{\varepsilon>0}$ of critical points of the Ambrosio-Tortorelli functional. Assuming a uniform energy bound, the sequence $\{(u_\varepsilon, v_\varepsilon)\}_{\varepsilon>0}$ converges in $L^2(Ω)$ to a limit $(u, 1)$ as $\varepsilon \to 0$, where $u$ is in $SBV^2(Ω)$. It was...
Since the alternating sign matrix conjecture, proposed by Mills, Robbins, and Rumsey in 1982, was proved by Zeilberger and Kuperberg, several refined enumerations have been considered. In particular, Behrend et al. obtained a quadruply refined enumeration by adding certain parameters. In this paper, we revisit the doubly refined...
In this expository article, we summarize what is known about maximum likelihood thresholds of Gaussian models, paying special attention to connections with rigidity theory.
Let W be a Weyl group. We define a class of irreducible representations of W that we call antispecial. They are in bijection with the constructible representations of W. We define an oriented graph structure on the set of antispecial representations or equivalently on the set of constructible representations of W. We describe...
Let $R$ be a finite product of integral domains and $D$ be a union of prime ideals (it is possible that $R$ is just an integral domain). Let $n \geq 1$ be a positive integer. This paper introduces the $n$-total graph of a $(R, D)$. The $n$-total graph of $(R, D)$, denoted by $n-T(R)$, is an undirected simple graph with vertex set $R$,...
Composite functions have been studied for over 40 years and appear in a wide range of optimization problems. Convex analysis of these functions focuses on (i) conditions for convexity of the function based on properties of its components, (ii) formulas for the convex conjugate of the function based on those of its components and (iii)...
We provide a closed formula for the graded Betti numbers in the linear strands of all powers of binomial edge ideals $J_G$ arising from closed graphs $G$ that do not have the complete graph $K_4$ as an induced subgraph. We show that these agree with the corresponding Betti numbers for the powers of the lexicographic initial ideal of...
We describe digraphs with topology which give dual representations of ortholattices. This is done via so-called dual Ploščica spaces of lattices. First, we improve the definition of Ploščica spaces from an earlier paper to give a straight and natural generalisation of the total order disconnectedness of Priestley spaces. Then we...