302 papers
This paper proposes and analyzes a convex estimator for the drift matrix of high-dimensional Lévy-driven Ornstein--Uhlenbeck processes under a low-rank-plus-sparse structure, establishing a non-asymptotic oracle inequality that demonstrates improved dimensionality dependence compared to purely sparse methods while accounting for discretization and truncation biases across various Lévy regimes.
This paper provides analytical predictions for the first-passage properties and spatial distributions of confined active Brownian particles by establishing a Siegmund duality between absorbing and hard-wall boundary conditions, revealing how active motion and initial orientation reduce mean first-passage times and lead to wall-accumulated stationary states.
By combining genetic evidence with a Markov chain analysis of historical drifter trajectories and transition path theory, this study demonstrates that the Eastern Pacific Barrier is weakly permeable to *Porites lobata* larvae, revealing a seasonal, ENSO-independent connectivity pathway from the Line Islands to Clipperton Atoll with travel times under five months.
This paper establishes that the supremum of the solution to a one-dimensional nonlinear stochastic partial differential equation, which encompasses models like the stochastic heat and linearized Cahn-Hilliard equations, admits a density with respect to Lebesgue measure by employing Malliavin calculus and the Bouleau-Hirsch criterion to overcome challenges related to the solution's argmax set and the nondegeneracy of its Malliavin derivative.
This paper proves that the grand canonical Gibbs state of an inhomogeneous two-dimensional interacting Bose gas converges to the renormalized Euclidean field theory in the high-density, short-range interaction limit, overcoming significant mathematical challenges posed by the need for divergent counterterm functions rather than simple scalars due to the presence of a trapping potential.
This paper extends Ding and Smart's 2020 Anderson localization results for random Schrödinger operators on the 2D lattice to non-identically distributed potentials by replacing the identical distribution assumption with uniform bounds on the essential range and variance, utilizing Bernoulli decompositions to establish a quantitative unique continuation principle and Wegner estimate that prove localization at the bottom of the spectrum.
This paper investigates a mean-field model of random multiplicative growth with redistribution, revealing that while strong migration prevents total localization under static growth rates, the addition of temporal noise induces a distinct partially localized phase that mitigates but does not eliminate extreme concentration, with implications for understanding population dynamics and wealth inequality.
This paper extends the Ziv-Merhav theorem on universal estimation of specific cross-entropy from multi-level Markov measures to a broader class of decoupled measures, including regular g-measures and equilibrium measures from statistical mechanics.
This paper analyzes the asymptotic behavior of a distributed ledger model with batch arrivals and random attachment delays by establishing that its key dynamics, such as the number of leaves, converge to a fluid limit described by delayed partial differential equations, which is further validated through stability analysis and simulations.
This paper proposes a discrete mathematical framework using coarse-grained partitions and categorical unification to quantify information loss in explainable AI, demonstrating that zero loss is an exceptional case and providing a method to optimize the trade-off between interpretability and informational fidelity.
This paper demonstrates that a noncentral Wishart mixture of noncentral Wishart distributions with identical degrees of freedom remains a noncentral Wishart distribution, a result used to derive the finite-sample distribution for testing random effects in two-factor and general factorial design models with multivariate normal data.
This paper develops a method to derive simple, analytically explicit upper or lower bounds for the survival probability of beneficial mutations in supercritical Galton-Watson processes by approximating their generating functions with fractional linear ones, and applies these results to model the evolution of quantitative traits under directional selection in finite populations.
This paper establishes a unified framework linking supersymmetry, Markov dualities, and shape-invariance exact solvability by analyzing the factorized structure of one-dimensional Fokker-Planck generators and their supersymmetric partners, extending these concepts to both diffusion processes and nearest-neighbor Markov jump processes.
This paper establishes that for planar random curves in domains with rough boundaries, the operations of taking weak limits and applying conformal maps commute, thereby confirming that the conformal image of a limit curve is the limit of the conformal images under minimal boundary regularity assumptions.
This paper establishes that the local scaling limit of multiple boundary-to-boundary branches in a uniform spanning tree is a local multiple SLE(2) process, a result derived by constructing a weighted martingale observable that relies on the discrete domain Markov property and the convergence of partition functions.
This paper proves that the height function of the six-vertex model with parameters and $1 \le c \le 2c > 2$.
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 presents a concise new computation of pairing probabilities for multiple chordal interfaces in various critical models by leveraging the convexity and a newly established uniqueness property of local multiple SLE measures.
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 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.