278 papers
This paper presents an almost purely combinatorial formula for Wilson loop expectations of the unitary Yang-Mills holonomy process on compact surfaces with arbitrary boundary conditions, expressing these expectations as a sum over highest weight assignments to curve complement components and applying this result to provide a concise proof of the Makeenko-Migdal equations.
This paper establishes the existence, uniqueness, and stability of solutions to the stochastic Benjamin-Bona-Mahony equation with multiplicative noise and derives optimal strong error estimates for a fully discrete finite element approximation under bounded noise, as well as sub-optimal convergence rates in probability for general noise via a localization technique.
This paper establishes a general sparse domination principle that respects the cancellative structure of functions across various measure spaces, including martingale and Euclidean settings, leading to new sharp weighted results for operators acting on spaces and a sparse characterization of the norm.
This paper introduces a variational framework based on the even-odd decomposition of support functions to define geometrically interpretable size-location correlation measures for set-valued processes, establishing their statistical properties under -mixing and enabling the analysis of dependence structures that are inaccessible to traditional point-based or selection-based methods.
This paper establishes the optimal loss exponent for context-sensitive binary hypothesis testing of i.i.d. observations under a multiplicative weight function by characterizing it as a weighted Chernoff information derived from the maximization of a log-normalizer within an exponential family of weighted geometric mixtures.
This paper introduces the -footrule coefficient, a new copula-based measure of negative association defined as the -distance to the countermonotonic copula, establishes its theoretical relationship with Gini's gamma and Spearman's footrule, and provides a statistically rigorous rank-based estimator with proven consistency and asymptotic normality.
This paper proves that, under a mild moment condition, the number of occurrences of a fixed rooted plane tree as a general subtree in a conditioned Galton--Watson tree is asymptotically normal with linear mean and variance, thereby confirming a conjecture by Janson and demonstrating that the result fails if the moment condition is violated.
This paper investigates the discrete-time Hawkes process by establishing its Large Deviation Principle, analyzing the limiting behavior of the associated arrival process, and demonstrating its application in modeling insurance claims.
This paper establishes the well-posedness of a complex -fractional Brownian bridge and proves the strong consistency and asymptotic distribution of its least squares parameter estimator for , revealing a unique two-dimensional limiting distribution with non-Cauchy marginals derived via complex Malliavin calculus.
This paper establishes a measure-theoretic framework for constructing Arveson systems from stationary factorizing measure types, providing a rigorous characterization of spatiality and a robust mechanism for generating type III systems via infinite products, which is applied to derive explicit type III random-set systems from the zero sets of Brownian motion.
This paper extends previous research on Poincaré and logarithmic Sobolev inequalities for perturbed measures to investigate analogous results for weaker functional inequalities, including weak and weighted variants, with applications to convolution products.
This paper establishes the existence and uniqueness of solutions to rough differential equations driven by tempered fractional Brownian motion with Hurst index by canonically lifting the noise to a geometric rough path and employing a Doss-Sussmann transformation combined with a greedy stopping time sequence, while also deriving quantitative growth bounds for the solutions.
This paper demonstrates that entropy acts as a driving force in various evolution equations because it characterizes the invariant measure of an underlying stochastic process, thereby unifying diverse examples from stochastic processes, gradient flows, and GENERIC systems under a single principle.
This paper establishes the existence and uniqueness of strong solutions for a stochastic differential equation driven by the sum of two correlated fractional Brownian sheets with distinct Hurst parameters, demonstrating that the additive noise regularizes the system to ensure well-posedness even under weak drift assumptions.
This paper introduces a novel method, incorporating new localization ideas inspired by stochastic partial differential equations, to compute the Hausdorff dimension of slow points in fractional Brownian motion, building upon recent work that established their existence.
This paper establishes the open-loop solvability and derives a closed-loop representation for a cone-constrained two-player zero-sum stochastic linear-quadratic differential game involving jump-diffusion systems with regime switching and random coefficients, utilizing forward-backward stochastic differential equations and newly proposed multidimensional indefinite extended stochastic Riccati equations with jumps.
This paper presents an elementary, self-contained proof of the Lovász Local Lemma that eliminates the need for conditional probabilities by relying solely on unconditional probability inequalities.
This paper extends functional central limit theorems for voter model occupation times on lattices to the case of spatially inhomogeneous product initial distributions by leveraging the duality with coalescing random walks and Donsker's invariance principle.
This paper establishes Gaussian and non-Gaussian limit theorems for non-linear additive functionals of stationary Gaussian fields with Gneiting-class non-separable covariance structures over anisotropically growing domains, demonstrating that these covariances are asymptotically separable in a cumulant sense to explicitly characterize convergence to either Gaussian or 2-domain Rosenblatt distributions based on long-range dependence conditions.
This paper establishes a quantitative Central Limit Theorem for continuous-time Stochastic Gradient Descent by employing Malliavin calculus and second-order Poincaré inequalities to derive explicit Wasserstein convergence rates driven by the learning rate magnitude, a result validated through numerical experiments.