309 papers
This paper demonstrates that the population-size distribution of supercritical Galton-Watson branching processes, in the asymptotic regime where the mean offspring number approaches one, can be effectively approximated by a compound Poisson-gamma distribution, a finding supported by numerical experiments and applicable to modeling cascaded multiplication processes.
This paper investigates the existence and form of Onsager-Machlup functionals for measures in dimensions , demonstrating that they recover the standard action in one and two dimensions (using enhanced distances) while proving degeneracy in three dimensions unless specific joint limits are considered.
This paper establishes a unified framework linking projective limits of probability measures to direct limits of their symmetry groups, demonstrating how this connection characterizes the symmetries of infinite point processes and provides a streamlined derivation of random graph limits, including graphons, graphexes, and models with bounded average degrees.
This paper derives an exact analytical three-dimensional channel impulse response for a fully absorbing spherical receiver under uniform drift by utilizing joint first-hitting time-location statistics and a Girsanov-based measure change to overcome previous symmetry-breaking limitations.
This paper introduces PANDAExpress, a novel algorithm that eliminates the impractical polylogarithmic factor of the original PANDA framework by employing a new probabilistic inequality and a dynamic hyperplane partitioning scheme, thereby achieving optimal, specialized-algorithm-level runtimes for conjunctive queries and disjunctive datalog rules under arbitrary degree constraints while maintaining full generality.
This paper proposes a stochastic gradient descent algorithm that dynamically maximizes revenue in a single-server queue with balking customers by using a novel Infinitesimal Perturbation Analysis procedure to estimate effective arrival rates based solely on observable joining behavior, thereby converging to the optimal price under mild regularity conditions.
This paper establishes a universal, asymptotically optimal concentration bound for sums of arbitrarily dependent random variables by leveraging the subadditivity of expected shortfall and constructing explicit extremal couplings, while providing practical conditions for deriving simple tail profiles based on convex transformation order comparisons.
This paper completes Le Cam's program by establishing a necessary and sufficient condition for the existence of nontrivial hypothesis tests between two sets of probability measures without requiring a common dominating measure, specifically by utilizing the closures of their convex hulls within the space of bounded finitely additive measures.
This paper establishes that biorthogonal ensembles with a specific derivative structure possess an explicit double contour integral correlation kernel, which serves as a foundation for asymptotic analysis and reveals two new classes of limit kernels: a deformed hard edge Bessel kernel and a kernel arising from Muttalib-Borodin type deformations.
This paper introduces a hierarchical Lorentz mirror model to prove normal transport in dimensions and proposes a universal $2/3$ mean-variance law for conductance, supported by numerical evidence suggesting this ratio is a signature of normal transport across dimensions.
This paper establishes a connection between the Bakry-Emery curvature of fractional Laplacian generators and fractional Brownian motion covariance, reformulating curvature inequalities as generalized eigenvalue problems that yield explicit bounds for the Cauchy case and demonstrate a scalar shift under confining drift.
This paper establishes a universality principle for visibility in hyperbolic space, proving that the critical intensity and mean visible volume for a Poisson process of -geodesic hyperplanes are independent of the interpolation parameter and identical to the case of totally geodesic hyperplanes.
This paper establishes concentration bounds for random Euclidean combinatorial optimization problems with -costs in dimensions by combining Poincaré inequalities with robust geometric mechanisms, while proposing a conjectural transfer principle to potentially extend these results to all .
This technical note extends the results of Kosygina, Mountford, and Peterson on generalized Pólya's urns from a specific weight function to a broader family of functions relevant to Tóth's study of polynomially self-repelling walks, thereby facilitating future research on the scaling limits of these processes.
This paper establishes the strong convergence with order $1/2$ for a geometric Euler-Maruyama scheme applied to stochastic differential equations on Riemannian manifolds and derives a corresponding Wasserstein bound for sampling via Riemannian Langevin dynamics.
This paper introduces cycle matrices as a basis for describing non-equilibrium properties in Markov chains, proving that the kernel of the interaction graph's incidence matrix is isomorphic to the space of anti-symmetric matrices with zero row sums.
This paper investigates continuous-time multi-armed bandits with random intervention times, providing explicit characterizations of the optimal Gittins index for arms evolving as Lévy processes and specific subclasses like spectrally negative Lévy processes and diffusion processes.
This paper derives the small ball probability for the collision local time of two independent symmetric -stable processes (with parameters satisfying ) by analyzing the asymptotic behavior of their moment generating function via contour integration.
This paper presents a Monte Carlo-based computational framework to analyze the steady-state distributions and stability of random differential equations with uncertain, multi-modal parameters, demonstrating its efficacy through a Rosenzweig-MacArthur predator-prey model that reveals complex, multi-modal equilibrium behaviors.
This paper demonstrates that while a continuous map into a metric space is of bounded variation if and only if its composition with every Lipschitz function is of bounded variation, this characterization fails for discontinuous maps in spaces like , infinite metric trees, and Laakso-type spaces, though it remains valid for ultrametric spaces without continuity assumptions.