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Regularization of the superposition principle: Potential theory meets Fokker-Planck equations

This paper advances the superposition principle for Fokker-Planck equations by constructing a full-fledged right Markov process under general measurability conditions, thereby resolving the open problem of establishing the strong Markov property and enabling new probabilistic solutions to the parabolic Dirichlet problem and flow constructions for both linear and nonlinear cases, including the generalized porous media equation.

Lucian Beznea, Iulian Cîmpean, Michael Röckner2026-03-06🔢 math

Optimization with Parametric Variational Inequality Constraints on a Moving Set

This paper investigates optimization problems constrained by parametric variational inequalities on moving sets by establishing the Lipschitz continuity of the solution function and automatic metric regularity, and proposes a Smoothing Implicit Gradient Algorithm (SIGA) that is proven to converge to a stationary point and validated through real-world portfolio management applications.

Xiaojun Chen, Jin Zhang, Yixuan Zhang2026-03-06🔢 math

Extending quasiconvex functions from uniformly convex sets

This paper investigates the extension of Lipschitz quasiconvex functions from closed convex sets with nonempty interior in finite-dimensional normed spaces, demonstrating that while Lipschitz extensions generally fail unlike in the convex case, the existence of uniformly continuous or continuous extensions is determined by specific geometric properties of the domain set.

Carlo Alberto De Bernardi, Libor Veselý2026-03-06🔢 math

What induces plane structures in complete graph drawings?

This paper investigates the conditions under which pairwise disjoint curves are unavoidable or avoidable in complete graph drawings, characterizing the resulting plane structures based on specific crossing rules for adjacent and non-adjacent curves.

Alexandra Weinberger, Ji Zeng2026-03-06🔢 math

Adaptive Sampling for Storage of Progressive Images on DNA

This paper proposes a cost-effective DNA storage system for progressive images that leverages Nanopore adaptive sampling to enable PCR-free random access, allowing users to retrieve specific resolution layers by selectively sequencing only the necessary oligos rather than the entire pool.

Xavier Pic, Nimesh Pinnamaneni, Raja Appuswamy2026-03-06🔢 math

Weighted Chui's conjecture

This paper establishes and proves the sharpness of a Newman bound counterpart for the Chui conjecture regarding Coulomb potentials generated by positive charges on the boundary of a unit ball, while also discussing a related problem involving charges within the unit disc.

Evgueni Doubtsov, Anton Tselishchev, Ioann Vasilyev2026-03-06🔢 math

Computing Scaled Relative Graphs of Discrete-time LTI Systems from Data

This paper presents methods to compute the Scaled Relative Graph (SRG) of discrete-time linear-time-invariant systems exactly from state-space models and exclusively from input-output data, while also introducing a robust SRG formulation capable of handling noisy trajectories.

Talitha Nauta, Richard Pates2026-03-06🔢 math

Drift parameter estimation in the double mixed fractional Brownian model via solutions of Fredholm equations with singular kernels

This paper proposes an effective numerical method for computing the maximum likelihood estimator of the drift parameter in a double mixed fractional Brownian motion model by reformulating the underlying operator equation as a Fredholm integral equation with a weakly singular kernel.

Yuliya Mishura, Kostiantyn Ralchenko, Mykyta Yakovliev2026-03-06🔢 math

Estimates of eigenvalues of elliptical differential problems in divergence form

This paper establishes universal eigenvalue estimates and derives bounds for the gaps between consecutive eigenvalues for coupled systems of second- and fourth-order elliptic differential equations in divergence form, encompassing operators such as the Lamé, Laplacian, and bi-Laplacian.

Marcio C. Araújo FIlho, Juliana F. R. Miranda, Cristiano S. Silva2026-03-06🔢 math

Ultralimits of Sobolev maps and stability of Dehn functions

This paper establishes that ultralimits of bounded Lipschitz maps extend naturally to Sobolev maps, a result used to prove the stability of Dehn functions under ultraconvergence of pointed length spaces and to provide a simpler proof characterizing spaces of curvature bounded above via isoperimetric inequalities.

Toni Ikonen, Stefan Wenger2026-03-06🔢 math

Hitting time for Hamilton cycles in pseudorandom graphs

This paper proves that for sufficiently pseudorandom graphs, the hitting time for the appearance of a Hamilton cycle (and $k$ edge-disjoint Hamilton cycles) coincides with the hitting time for reaching minimum degree 2 (or $2k$), thereby resolving long-standing questions by Alon, Krivelevich, and Frieze and establishing sharp thresholds for these properties.

Yaobin Chen, Yu Chen, Seonghyuk Im + 1 more2026-03-06🔢 math

Worst-case $L_p$ -approximation of periodic functions using median lattice algorithms

This paper proves that a median lattice algorithm, which aggregates multiple rank-1 lattice sampling rules via componentwise median, achieves high-probability, nearly optimal worst-case $L_p$ -approximation rates for multivariate periodic functions in weighted Korobov spaces, with dimension-independent constants for $L_\infty$ under specific weight summability conditions.

Zexin Pan, Mou Cai, Josef Dick + 2 more2026-03-06🔢 math

On Ehrhart theory for tropical vector bundles

This paper establishes a combinatorial Hirzebruch-Riemann-Roch theorem for tropical vector bundles on toric varieties using Khovanskii-Pukhlikov theory and confirms that the Euler characteristic equals the rank of global sections for tautological bundles associated with matroids.

Suhyon Chong, Kiumars Kaveh2026-03-06🔢 math

Besov regularity of solutions to the Dirichlet problem for the Bessel $(p,s)$ -Laplacian

This paper establishes global Besov regularity estimates for weak solutions to the Dirichlet problem of a fractional $p$ -Laplacian defined via the Riesz fractional gradient by combining Lions-Calderón spaces, Besov embeddings, and an adapted Nirenberg difference quotient method, yielding specific regularity indices that depend on the interplay between the order $s$ and the exponent $p$ in both superquadratic and subquadratic regimes.

Juan Pablo Borthagaray, Leandro M. Del Pezzo, José Camilo Rueda Niño2026-03-06🔢 math

Andrews--Gordon type identities with parity restrictions through particle motion

This paper employs the particle motion bijection to establish new $q$ -series identities of the Andrews--Gordon type with parity restrictions on part multiplicities, thereby generalizing previous results and providing a simplified proof of a recent identity related to Ariki--Koike algebras.

Jehanne Dousse, Jihyeug Jang2026-03-06🔢 math

Maximum of sparsely equicorrelated Gaussian fields and applications

This paper investigates the extreme values of sparse, equicorrelated Gaussian fields on a triangular grid to identify the correlation threshold where the standard Gumbel law fails, utilizing the Chen-Stein method to resolve open questions in high-dimensional statistics and multiple testing.

Johannes Heiny, Tiefeng Jiang, Tuan Pham + 1 more2026-03-06🔢 math

Riemannian Geometry of Optimal Rebalancing in Dynamic Weight Automated Market Makers

This paper establishes that the optimal rebalancing trajectory for Dynamic Weight Automated Market Makers corresponds to a geodesic under the Fisher-Rao metric (SLERP in Hellinger coordinates), thereby proving that the recursive AM-GM bisection heuristic used in prior work lies exactly on this loss-minimizing path.

Matthew Willetts2026-03-06🔢 math

Teichmüller space of a closed set in the Riemann sphere

This paper establishes the conformal naturality of the Lieb isomorphism and the real-analyticity of the Douady-Earle section for Teichmüller spaces of closed sets in the Riemann sphere, utilizing these results to prove that families of Jordan curves with holomorphically varying marked points vary real-analytically as quasiconformal images.

Xinlong Dong, Arshiya Farhath. G, Sudeb Mitra2026-03-06🔢 math

Conditional asymptotic stability of solitary waves of the Euler-Poisson system on the line

This paper establishes the conditional asymptotic stability of solitary waves for the Euler-Poisson system on the line by combining virial inequalities and Kato smoothing to prove that solutions remaining close to a soliton converge to it as time approaches infinity.

Junsik Bae, Scipio Cuccagna, Masaya Maeda2026-03-06🔢 math

Bayes with No Shame: Admissibility Geometries of Predictive Inference

This paper demonstrates that predictive inference is governed by four distinct, pairwise non-nested admissibility geometries—Blackwell risk dominance, anytime-valid supermartingales, marginal coverage, and Cesàro approachability—each offering a unique certificate of optimality and proving that admissibility is irreducibly relative to the chosen criterion rather than a universal property.

Nicholas G. Polson, Daniel Zantedeschi2026-03-06🔢 math

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