287 papers
This paper establishes that for discretely observed oscillating Brownian motion, the maximum likelihood estimator of the self-organized criticality level achieves -consistency and converges stably to a bivariate Poisson-type distribution, despite the non-standard challenge posed by the discontinuity of the transition density at the true parameter.
This paper establishes the existence of equilibria for a class of Mean Field Games involving reflected stochastic differential equations by utilizing the framework of relaxed controls and martingale problems.
This paper establishes the existence and uniqueness of solutions to reflected generalized backward stochastic differential equations (GRBSDEs) with RCLL random obstacles under a general filtration supporting Brownian motion and an independent integer-valued random measure, while also linking these solutions to optimal control problems over stopping times.
This paper introduces and analyzes a divide-and-conquer algorithm for quantizing one-dimensional probability distributions, establishing a universal Wasserstein-1 error bound and demonstrating through numerical experiments that the method achieves optimal convergence rates while offering superior stability under arithmetic operations compared to existing schemes.
This paper theoretically analyzes the Bergman determinantal point process to optimize its simulation by constructing restricted variants, establishing optimal transport inequalities for truncation errors, determining the optimal number of points with deviation bounds, and providing general deviation results for determinantal point processes.
This paper establishes the Mosco-convergence of Cheeger energies on Gromov-Hausdorff converging spaces satisfying curvature-dimension conditions by employing a Lagrangian approach that combines Wasserstein geodesic stability with nonsmooth calculus duality, thereby ensuring the continuity of Neumann eigenvalues even in infinite-dimensional settings.
This paper extends the probabilistic construction of Kähler-Einstein metrics to Fano manifolds with non-discrete automorphism groups by introducing Gibbs polystability and symmetry-breaking via moment map constraints, conjecturing its equivalence to metric existence and the emergence of unique metrics in the large-N limit, while proving these results for log Fano curves and deriving a strengthened logarithmic Hardy-Littlewood-Sobolev inequality with optimal stability constants.
This paper characterizes the transition of first arrival position channel noise from heavy-tailed Cauchy to exponentially decaying distributions under nonzero drift, identifying a characteristic propagation distance that delineates diffusion-dominated and drift-dominated regimes while demonstrating that Gaussian approximations fail to capture communication potential in low-drift environments.
This paper establishes an up-to-constant estimate for the critical two-point function restricted to a half-space in high-dimensional Bernoulli percolation (), thereby completing prior work by Chatterjee, Hanson, and Sosoe and resolving a specific question posed by Hutchcroft, Michta, and Slade.
This paper investigates a once-reinforced random walk on the half-line and establishes the limiting behaviors for all moments of its range.
This study employs a stochastic-process model to demonstrate that the optimal autocorrelation of time-series signals for solving multi-armed bandit problems depends on the reward environment, with negative autocorrelation being advantageous in reward-rich settings and positive autocorrelation in reward-poor ones, while performance remains independent of autocorrelation when the sum of winning probabilities equals one.
This paper establishes the existence of equilibria for non-Markovian mean-field games with unbounded controls and quadratic running costs using a weak formulation approach grounded in new stability results for quadratic-growth generalized McKean-Vlasov BSDEs, thereby removing previous restrictions on model parameter boundedness and time horizons.
This paper establishes the precise asymptotic variance and a Gaussian central limit theorem for the log-partition function of the Sherrington-Kirkpatrick spin glass model in the critical regime where the inverse temperature approaches the critical point at a rate of .
This paper introduces "Blackwells Demon," a thought experiment demonstrating that under specific restrictive conditions involving a complex environment, one can predict the direction of a random walk with a success probability greater than 1/2 by exploiting inhomogeneities in a statistically homogeneous system, analogous to how Maxwell's Demon exploits molecular speed variations.
This paper provides a more elementary proof of the nonasymptotic universality laws established by Brailovskaya and van Handel, demonstrating that the spectral statistics of independent sums of random matrices mirror those of Gaussian matrices with matching first- and second-order moments, by utilizing a novel implementation of the method of exchangeable pairs.
This paper investigates the long-time asymptotic behavior of multivariate Hawkes processes with power-law decaying interactions, employing a combination of short-range interaction techniques, -stable law properties, and Tauberian theorems to model realistic systems like neural networks with long-range connections.
This paper demonstrates that while the "spectral density" derived from Gurau's resolvent trace yields valid probability measures on average for certain random tensor ensembles, it fails to correspond to a probability measure for individual deterministic tensors, thereby proving it is not a pointwise-defined probability distribution.
This paper investigates the Martin boundary of space-time Markov chains associated with finitely supported random walks to establish structural connections between various compactifications and harmonic function boundaries, ultimately demonstrating that the noncommutative Shilov boundary of the associated tensor algebra coincides with its Toeplitz -algebra.
This paper establishes the almost sure Hausdorff dimension of the images and graphs of a broad class of random complex series, which encompasses famous deterministic functions like the Weierstrass and Riemann functions, thereby providing a probabilistic framework to predict the exact dimension values of their deterministic counterparts.
This paper establishes the first large deviation principle for convolutional neural networks in the infinite-channel regime, characterizing the asymptotic behavior of conditional covariance matrices and posterior distributions under Gaussian priors while also providing streamlined proofs for their Gaussian equivalence and concentration.