6977 papers
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 for multiplicative noise and $1$ for additive noise, while also demonstrating the convergence of the stochastic -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.
This paper employs an inverse optimization framework on NFL play-by-play data to demonstrate that coaches' historically conservative fourth-down decisions are consistent with optimizing low quantiles of future value, revealing that their risk preferences have become more tolerant over time and vary based on field position.
This paper establishes the strong convergence rate of an Euler-Maruyama numerical scheme for one-dimensional stochastic differential equations with distributional drifts in Hölder-Zygmund spaces, supported by theoretical bounds and numerical implementation.
This paper establishes that homogenisation and renormalisation commute for the two-dimensional periodic generalised parabolic Anderson model by introducing a novel solution ansatz to handle variable coefficients and demonstrating that the standard model can be constructed via para-controlled calculus without commutator estimates.
This paper constructs analogs of Khovanov-Jacobsson classes and the Rasmussen invariant for links in the boundary of smooth oriented 4-manifolds by utilizing skein lasagna modules derived from equivariant and deformed link homology, while establishing non-vanishing results, decomposition theorems, and conditions for extending functoriality to immersed cobordisms.
This paper proposes two novel single-loop zeroth-order primal-dual algorithms, ZO-PDAPG and ZO-RMPDPG, that achieve state-of-the-art iteration complexity guarantees for solving nonconvex-(strongly) concave minimax problems with coupled linear constraints under both deterministic and stochastic settings.
This paper proves a Gersten-type conjecture for étale sheaves, including étale logarithmic Hodge-Witt sheaves and -adic Tate twists, over henselian local rings of normal crossing varieties in positive characteristic, and applies this result to establish a relative version of the conjecture for -adic étale Tate twists over semistable families in mixed characteristic as well as a generalization of Artin's theorem on Brauer groups.