308 papers
This paper introduces a novel numerical method that combines a functional equation for the Laplace-Stieltjes transform with a moment-matching technique to efficiently and stably compute the density of the Kesten-Stigum limit for supercritical Galton-Watson processes with arbitrary offspring laws.
This paper establishes quantitative pathwise entropy bounds for a stochastic 2D vortex model on the whole space under moderate interactions by combining Donsker-Varadhan inequalities with localization techniques, and subsequently derives new energy estimates for the convergence of particle systems to the limiting process.
This paper applies a probabilistic machine learning framework to analyze Collatz stopping times up to $10^7$, demonstrating that a Bayesian hierarchical Negative Binomial regression outperforms a mechanistic odd-block generator in predictive likelihood while revealing that low-order modular structure significantly drives the observed heterogeneity.
This paper resolves a long-standing open problem by establishing a universal central limit theorem for both smooth and numerical statistics of intersection currents arising from independent Gaussian holomorphic sections in arbitrary codimensions, thereby fully extending the 2010 Shiffman–Zelditch theorem through a novel geometric framework that adapts Wiener chaos and Feynman diagram techniques to random currents on complex manifolds.
This paper characterizes fractional Malliavin-Watanabe-Sobolev spaces for all by establishing a criterion based on the integrability and fractional differentiability properties of the -transform's Bargmann-Segal norm, thereby bridging Malliavin calculus with white noise analysis and providing practical tools for analyzing objects like Donsker's delta and self-intersection local times.
This paper establishes two-sided heat kernel estimates for "book-like" graphs, which are formed by gluing together multiple pieces satisfying the parabolic Harnack inequality along a common set of vertices, with results robust enough to accommodate various structural perturbations.
This paper proves that the coordinate change formula for the Liouville quantum gravity distance function holds almost surely for all conformal maps simultaneously, thereby rigorously establishing the definition of a quantum surface as a random equivalence class of domains equipped with both LQG area and distance measures.
This paper proposes and analyzes two consistent and asymptotically normal estimators for the edge existence probability of a dynamic Erdős–Rényi graph by observing only the population distribution of individuals moving across its vertices, without direct access to the graph's structure.
This paper establishes a dimension-independent lower bound on the cotype constant for normed spaces generated by random polytopes with Gaussian vertices, demonstrating that under specific density conditions on the number of vertices relative to dimension, these spaces satisfy a cotype inequality with high probability.
This paper establishes a BBP phase transition for a doubly sparse deformed Wigner ensemble, proving that sparse signal vectors with strength greater than one generate outlier eigenvalues and correlate with top eigenvectors in the supercritical sparsity regime, thereby generalizing previous results to models where both the noise matrix and signal vectors are sparse without requiring specific relationships between their sparsity levels.
This paper presents a probabilistic solution for linear-quadratic optimal control problems with state constraints, providing a representation for the value function and an explicit optimal control that keeps the system within a specified domain while minimizing quadratic control costs.
This paper demonstrates that a suitable multiplicative Stratonovich noise perturbation can restore well-posedness to the Cauchy problem of a weakly hyperbolic operator with double involutive characteristics, whereas its deterministic counterpart is restricted to well-posedness only within Gevrey classes $1 \leq s < 2$.
This paper establishes quantitative error estimates linking microscopic fluctuations in interacting particle systems and regularized stochastic PDEs to their macroscopic mobilities, while also characterizing the asymptotic behavior of fluctuation structures in irregular Dean-Kawasaki type equations through renormalized kinetic solutions.
This paper establishes novel and strictly sharper Berry-Esseen bounds for the second moment estimator of asymptotically stationary Gaussian processes observed at high frequency, specifically deriving convergence rates in total variation, Kolmogorov, and Wasserstein distances for the drift parameters of Gaussian Ornstein-Uhlenbeck processes.
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.
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.
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.
This paper provides a rigorous construction of Dyson Brownian motion on a rectifiable Jordan curve and analyzes its fundamental properties, including the associated Fokker-Planck-Kolmogorov equation, convergence to the stationary Coulomb gas distribution, low-temperature large deviations, and the limiting McKean-Vlasov equation in the many-particle regime.
This paper develops a calculus of space-time controlled fields to establish a unified composition rule and a rough stochastic Itô-Wentzell formula for evaluating random fields along rough semimartingales, motivated by recent advances in Itô-Alekseev-Gröbner and related interpolation identities.
This paper establishes a free probability analogue of Obata's rigidity theorem by proving that under a non-commutative curvature-dimension condition, the saturation of Voiculescu's free Poincaré inequality forces the underlying von Neumann algebra to split off a freely complemented semicircular component, thereby extending classical Gaussian splitting phenomena to the non-commutative setting.