5617 papers
This paper introduces and analyzes a broad class of continuous directed polymers in driven by Gaussian environments, establishing their structural properties, proving a sharp measure-theoretic dichotomy regarding their relation to Wiener measure, and demonstrating diffusive behavior in high dimensions and high temperatures, thereby extending the Alberts--Khanin--Quastel framework to higher-dimensional settings.
Inspired by R. Heitmann's proof of the Direct Summand Conjecture and G. Faltings' normalized length, this paper establishes new results on local cohomology modules in mixed characteristic using the Frobenius map, with significant implications for the study of splinters.
This paper introduces a new poset property defined via a variation of the Banach-Mazur game that strengthens -strategic closedness, proves that the Proper Forcing Axiom (PFA) is preserved under forcing with such posets, and applies this result to reproduce Magidor's theorem on the consistency of PFA with weak square principles while distinguishing the property from -operational closedness.
This paper proposes and analyzes a novel class of modified averaged vector field methods that simultaneously preserve multiple invariants for conservative Stratonovich stochastic differential equations, proving their mean square convergence order of 1 under commutative noises and demonstrating their superiority in long-time simulations through numerical experiments.
This paper establishes the probabilistic superiority of stochastic symplectic methods over non-symplectic ones by proving that the former asymptotically preserve the large deviations principles governing the exponential decay of hitting probabilities for the mean position and velocity of stochastic Hamiltonian systems, a result demonstrated via the Gärtner–Ellis theorem on the linear stochastic oscillator.
This paper determines the all-genus Hodge-Gromov-Witten theory for smooth hypersurfaces in weighted projective spaces defined by chain, loop, or general invertible polynomials, providing the first genus-zero Gromov-Witten invariants for non-Gorenstein ambient spaces where convexity fails.
This paper establishes that symplectic discretizations, including spectral Galerkin spatial semi-discretization and temporal full discretization, weakly asymptotically preserve the large deviations principle of the stochastic linear Schrödinger equation, thereby providing an effective numerical approach for approximating the LDP rate function in infinite-dimensional spaces.
This paper establishes convergence rates for scalable pseudo-likelihood-based -estimators of random graph models with dependent edges and increasing parameter dimensions, addressing challenges like phase transitions and near-degeneracy through a novel class of generalized -models.
This paper presents a convergence analysis for minimum action methods coupled with finite difference schemes, establishing that the convergence orders of the discrete Freidlin-Wentzell action functional are $1/21\theta$-method for small-noise stochastic differential equations in the context of large deviations.
This paper establishes the convergence of the probability density for a fully discrete finite difference method solving the stochastic Cahn--Hilliard equation with multiplicative space-time white noise by introducing a novel localization argument to overcome the non-Lipschitz drift and partially resolving an open problem regarding the numerical computation of the solution's density.
This paper introduces a unified definition of Anosov representations for relatively hyperbolic groups that encompasses various existing notions of geometrically finite behavior and proves their stability under deformations satisfying specific dynamical conditions on peripheral subgroups.
This paper proposes a co-design framework that jointly optimizes communication topology and differential privacy levels in multi-agent formation control to balance privacy protection, network connectivity, and steady-state performance.
This paper introduces and analyzes the Generalized Multiplicative Gradient (GMG) method for solving convex optimization problems over symmetric cones with non-Lipschitz gradients, establishing an convergence rate through novel theoretical results and demonstrating its superior computational complexity compared to other first-order methods across several key applications.
This paper establishes that the most general "reasonable category of strong vector spaces" admitting formal infinite sums is equivalent to the category of ultrafinite summability spaces, characterizing it as a specific orthogonal subcategory of and analyzing its monoidal closed structures in relation to other categories of topological vector spaces.
This paper establishes the Freidlin--Wentzell large deviations principle for the stochastic Cahn--Hilliard equation with small noise and proves the convergence of the one-point large deviations rate function for its spatial finite difference method by utilizing -convergence of objective functions and overcoming non-Lipschitz drift challenges through discrete interpolation inequalities.
This paper introduces a distributionally robust framework for the single airport ground holding problem under Wasserstein ambiguity sets, featuring a novel hybrid algorithm that combines Kelly's cutting plane method with the integer L-shaped method to achieve significant computational speedups while enhancing decision-making resilience against capacity distribution shifts.
This paper establishes the central limit theorem for the temporal average of the backward Euler–Maruyama method applied to stochastic ordinary differential equations with super-linearly growing drift coefficients, deriving the result through direct analysis for sub-optimal deviation orders and via a Poisson equation approach for the optimal strong order.
This paper solves the Dirichlet problem for minimal Killing graphs over non-compact domains in 3-manifolds fibered by a Killing vector field, establishing Collin-Krust type estimates, proving uniqueness results in the Heisenberg group, and demonstrating the removability of isolated singularities.
This paper proposes and analyzes a simultaneous M-estimator for detecting a change point and recovering diffusivity values in a stochastic heat equation with space-dependent diffusivity, demonstrating that the change point converges at rate while diffusivity constants converge at rate based on local spatial measurements.
This paper establishes canonical bundle formulas for fibrations of curves with arithmetic genus one in characteristic , distinguishing between separable and inseparable cases, and applies these results to prove that a klt pair with a nef anti-log canonical divisor and a relative dimension one Albanese morphism is a fiber space over its Albanese variety.