271 papers
This paper introduces a generic sketching scheme for estimating -moments in the turnstile streaming model by hashing indices to Lévy processes, leveraging the Lévy-Khintchine representation theorem to unify existing methods and characterize the tractability of a broad class of functions, including nearly periodic and heterogeneous cases.
This paper introduces a novel Monte Carlo method for estimating by tossing a coin, which utilizes a new interpretation of derived from Catalan-number series identities.
This paper extends the concept of -mixing to set-valued random sequences in Banach spaces and establishes several strong laws of large numbers for such sequences, demonstrating the naturalness and sharpness of the underlying hypotheses through illustrative examples.
This paper constructs specific classes of strictly stationary, reversible Markov chains with finite second moments where the central limit theorem fails, thereby investigating the limited extent to which reversibility aids central limit theory under various mixing rates, particularly contrasting power-type and sub-exponential scenarios.
This paper establishes the continuity of asymptotic entropy for random walks on wreath products (where is any countable group and is a hyper-FC-central group with a cubic-growth subgroup) by proving the continuity of non-return probabilities and demonstrating that weak continuity of harmonic measures implies entropy continuity, thereby extending known results to new classes of groups including linear and groups.
This paper investigates long-range one-dimensional internal diffusion-limited aggregation, establishing that clusters formed by random walks with finite variance converge to a nearly symmetric contiguous block (improving previous moment conditions), while those driven by walks in the domain of attraction of symmetric -stable laws ($1 < \alpha < 2$) form a contiguous block that occupies only a fraction of the total sites.
This paper investigates the contact process on dynamical random trees with degree-dependent edge updates, establishing sufficient conditions for a positive critical infection rate on general graphs and characterizing phase transitions—specifically proving strong survival for any infection rate under certain offspring distributions and providing a complete phase transition analysis for power-law trees with product kernels.
This paper investigates how key properties of probability monads, including their Kleisli laws, monoidal structures, and affinity, arise from their codensity presentations, establishing new universal properties for these monads and characterizing their tensor products via Day convolution while highlighting the limitations of the Giry monad on standard Borel spaces.
This paper provides a complete description of the Poisson boundary for wreath products under conditions where lamp configurations stabilize and the projected measure on is Liouville, thereby resolving a long-standing open question regarding the boundary for () with finite first moment measures.
This paper proposes and analyzes a two-grid penalty approximation scheme for decoupled Markovian doubly reflected BSDEs, which overcomes error amplification from obstacle evaluation by simulating the forward process on a finer grid, thereby establishing explicit error bounds and optimal tuning rules to achieve a target convergence rate of .
This paper establishes that the space of infinite circle patterns in the Euclidean plane parameterized by discrete harmonic functions of finite Dirichlet energy forms an infinite-dimensional Hilbert manifold homeomorphic to the Sobolev space of half-differentiable functions, equipped with a Riemannian metric derived from a hyperbolic volume functional that relates to a symplectic form via an analogue of the Hilbert transform, thereby connecting these patterns to the Weil-Petersson class of the universal Teichmüller space.
This paper establishes uniform concentration inequalities for random matrices with -subexponential tails (), extending optimal subgaussian results to heavier-tailed distributions and providing new guarantees for robust high-dimensional inference and dimension reduction.
This paper extends the definition of the multidimensional Dickman distribution to vector-valued random elements characterized as fixed points of a specific affine transformation, proving their infinite divisibility and operator selfdecomposability while identifying cases where they emerge as limiting distributions.
This paper presents a vector generalization of the curvature-corrected Cramér-Rao bound for multivariate parameters in the nonasymptotic regime, utilizing extrinsic geometry and sum-of-squares relaxations to derive directional and matrix-valued refinements that offer more faithful estimation limits than classical second-order corrections, as demonstrated through curved Gaussian and spherical multinomial models.
This paper presents a geometric refinement of the classical Cramér-Rao bound in the non-asymptotic regime by leveraging the extrinsic curvature of the statistical model manifold's square root embedding to derive tighter, curvature-aware lower bounds on estimator variance.
This paper presents two novel, short proofs for the sharp uniform-in-diffusivity mixing rate of passive scalars in parallel shear flows with weak molecular diffusion, utilizing stochastic integration-by-parts to establish optimality under minimal regularity and a dynamical systems approach to provide a new perspective on shear-induced mixing.
This paper extends the theoretical framework for estimating diffusive flux into stochastically gated tubes by deriving an explicit formula that remains accurate for non-narrow geometries and varying diffusivities, overcoming challenges related to complex 3D geometry and multiplicative noise.
This paper characterizes the Palm distributions of superposed independent point processes through a mixture representation, enabling new statistical inference strategies for minimum contrast estimation of corrupted processes and likelihood-based analysis of shot noise Cox processes.
This paper investigates the asymptotic behavior of the entrance probability for discounted aggregate claims in a multivariate risk model with constant interest force and dependent subexponential claims over both finite and infinite time horizons, ultimately applying these findings to analyze ruin probabilities in models with Brownian perturbations.
This paper re-establishes the existence of level-2 rough integrals for controlled rough paths using a point-removal method, derives a new a priori estimate, and proves a universal limit theorem for rough differential equations driven by controlled rough paths, thereby extending the classical theory.