281 papers
This paper establishes that the asymptotic distribution of quadratic forms for self-normalized heavy-tailed random vectors is determined solely by the diagonal entries of the matrix and the stability index , a result applied to derive the atom-free nature of the -heavy Marčenko--Pastur law for heavy-tailed sample correlation matrices.
This paper develops a comprehensive Malliavin calculus for the Dirichlet–Ferguson process on a general phase space by deriving explicit chaos expansions, establishing fundamental operators and rules, and applying the framework to characterize the Fleming–Viot process and prove a Poincaré inequality.
This paper proves that in a general round-robin tournament model with equally strong players, the largest scores are asymptotically almost surely distinct provided that grows to infinity while satisfying the condition .
This paper demonstrates that the focusing effect of rare fluctuations onto an optimal path, previously established in Langevin dynamics, also persists in discrete-time Markov jump processes through a framework combining large deviation theory and time reversal.
This paper establishes necessary and sufficient conditions for the Markov property of a coupled virus-like evolving population model driven by mutually-exciting Hawkes processes, utilizing this property to derive convergence results and demonstrate a phase transition at a critical fitness level.
This paper introduces a new class of non-equal volume partitions that achieve a lower expected star discrepancy and improved upper bounds compared to classical jittered sampling, thereby providing a theoretical foundation for their use in high-dimensional numerical integration.
This monograph offers a rigorous theoretical and methodological overview of probabilistic inference and learning with Stein's method, detailing the construction and properties of Stein discrepancies, their connection to Stein variational gradient descent, and providing precise definitions and proofs.
This paper establishes a unified security threshold for interactive authentication over noisy quantum channels by upper-bounding Eve's forgery probability with a Holevo-type quantity derived from min-entropy estimates, thereby proving the protocol is both -secure and composable against forgery and key leakage.
This paper develops quantitative tools to study random minimum spanning trees (MST) generated by assigning independent edge weights from arbitrary distributions, addressing the gap in mathematical understanding between these practical algorithms and the more extensively studied uniform spanning trees.
This paper resolves a question posed by Steinerberger by proving that the factor in the two-dimensional Green–Wasserstein inequality is necessary and cannot be removed while maintaining a uniform remainder for point sets on compact connected surfaces.
This paper proposes an Euler-type framework with equidistant step sizes for time-changed stochastic differential equations, establishing that both the standard and truncated Euler–Maruyama methods achieve strong convergence rates close to under global Lipschitz and relaxed Khasminskii-type conditions, respectively, which contrasts with the classical $1/2$ order found in methods using random step sizes.
This paper establishes the theory of the discrete periodic Pitman transform by proving its braid relations, defining an infinite symmetric group action, and demonstrating multi-path invariance for periodic polymer models through a new inhomogeneous Burke property.
This paper establishes that multiparameter multidimensional Markov processes time-changed by an independent additive subordinator form a Feller evolution with a specific pseudo-differential generator, deriving explicit symbol representations for Ornstein-Uhlenbeck processes and applying the framework to finance-inspired factor-based models.
This paper establishes the existence and uniqueness of mild solutions for a three-dimensional Boussinesq-type system with Dirichlet boundary noise, proving that for sufficiently small initial data, the solution exists globally with high probability ($1 - C\varepsilon$) up to a stopping time.
This paper establishes the almost sure convergence of the logarithm of the largest fragment size in positive-index self-similar fragmentation processes to a precise asymptotic expansion involving a second-order correction term, significantly refining previous results by Bertoin.
This paper establishes uniform regularity estimates for the principal Dirichlet eigenfunctions of both discrete random walks and continuous Brownian motion in Lipschitz domains by employing a novel probabilistic approach combining Feynman-Kac representations, gambler's ruin estimates, and a new "multi-mirror" coupling, while also reviewing convergence results between the discrete and continuous eigenfunctions.
This paper characterizes the solution spaces of perturbed linear stochastic Volterra equations in discrete and continuous time, establishing that while -summable perturbations are necessary and sufficient for almost sure -summability in the discrete case, the continuous case allows for almost sure -integrability even with non-integrable perturbations, a result proven via discretization and extended to analyze asymptotic convergence and broader functional differential equations.
This paper mathematically proves that in three-dimensional space, the Cauchy walk (Lévy exponent ) uniquely achieves scale-invariant, near-optimal detection across diverse target sizes and shapes by transitioning from volume-dominated to surface-area-dominated search strategies, thereby establishing a rigorous foundation for the Lévy flight foraging hypothesis in 3D.
This paper proves an asymptotically optimal bound for the concentration function of a sum of independent integer random variables, confirming that the sum's maximum point probability is bounded by that of a corresponding sum of minimal-variance variables when the total variance is sufficiently large, thereby extending the result to separable Hilbert spaces.
This paper establishes sharp rates of propagation of chaos for McKean-Vlasov equations with non-linear measure-dependent coefficients, applying these results to derive uniform-in-time convergence guarantees for mean field Langevin dynamics, control, and games by combining the BBGKY hierarchy with weak propagation techniques.