309 papers
This paper establishes a free probability analogue of Obata's rigidity theorem by proving that under a non-commutative curvature-dimension condition, the saturation of Voiculescu's free Poincaré inequality forces the underlying von Neumann algebra to split off a freely complemented semicircular component, thereby extending classical Gaussian splitting phenomena to the non-commutative setting.
This paper establishes that the chromatic number of the random Borsuk graph transitions from being -colourable to requiring more than colours when the average degree is constant for $2 \leq k \leq dk=2$ case via continuum AB percolation.
This paper establishes that uniform random triangulations with boundaries in high genus converge locally to half-plane hyperbolic triangulations when rooted at a boundary edge and to the Planar Stochastic Hyperbolic Triangulation when rooted at a random edge, providing a new construction of the former and a proof technique independent of the Goulden-Jackson recurrence.
This paper establishes that the tail probabilities of sums of independent uniform random variables are dominated by a Gaussian tail with matching variance, determining the precise multiplicative constant required for this sharp stochastic domination.
This paper establishes novel criteria for the continuity of Itô integration under Skorokhod's J1 and M1 topologies, demonstrates that M1 tightness implies J1 tightness for local martingales under mild conditions, and applies these findings to derive weak convergence results for anomalous diffusion models driven by continuous-time random walks.
This paper investigates a discrete model of a heterogeneous elastic line with random springs, demonstrating that when the spring constant distribution follows a power law with exponent , the system exhibits anomalous scaling driven by sample-to-sample fluctuations and abrupt shape jumps, a finding that challenges previous theoretical predictions and is validated by numerical simulations.
This paper establishes central and non-central limit theorems for functionals of stationary Gaussian fields integrated over growing product domains, analyzing both separable covariance structures with quantitative bounds for Hermite polynomials and extensions to Gneiting-class or additively separable covariances.
This paper establishes an ergodic theorem for Markov chains indexed by trees of arbitrary shape under specific geometric and regularity conditions, while also demonstrating that for stationary and reversible chains, the linear tree structure minimizes the variance of empirical average estimators.
This paper extends Bobkov and Chistyakov's upper bounds on concentration functions to a multivariate entropic setting using pointwise density estimates, thereby deriving sharp bounds on the volumes of noncentral sections of isotropic convex bodies.
This paper derives an explicit, non-asymptotic formula for the expected Lipschitz-Killing curvatures of excursion sets for arbitrary left-invariant Gaussian spin spherical random fields on with respect to an arbitrary metric, providing a general framework applicable to non-degenerate Gaussian fields on three-dimensional compact Riemannian manifolds for analyzing Cosmic Microwave Background polarization.
This paper establishes that low-degree polynomial tests can distinguish between correlated sparse stochastic block models and independent Erdős-Rényi graphs if and only if the subsampling probability exceeds the minimum of Otter's constant and the Kesten-Stigum threshold, thereby identifying a sharp computational transition for detection and partial recovery.
This paper extends the coding of measured -trees to càdlàg functions using Skorokhod's topology to demonstrate that while tree rotation acts as a dilation for critical Bienaymé trees with Gaussian offspring limits, it yields a different scaling limit encoded by spectrally positive -stable Lévy processes when the offspring distribution falls in the domain of attraction of an -stable law with .
This paper defines a fractional Ito stochastic integral with respect to a randomly scaled fractional Brownian motion using an -transform approach, establishes the corresponding Ito formula, and applies it to investigate generalized time-fractional evolution equations.
This paper investigates the one-dimensional stochastic porous medium equation with additive white noise, combining functional renormalization group predictions and extensive numerical simulations to characterize its growth exponents, anomalous scaling, and multiscaling properties, while identifying its stationary measure with a random walk model related to a Bessel process.
This paper proposes a correlation-based metric and a simple common-neighbor clustering algorithm to achieve exact, almost exact, and weak recovery of small, heterogeneously-sized communities in the planted partition model, overcoming the limitations of traditional methods in highly unbalanced settings.
This paper extends the classical sharp upper bound on central hyperplane sections of a regular simplex to a probabilistic framework involving negative moments of centered log-concave random variables, revealing a phase transition in the extremizing distributions for new sharp reverse Hölder-type inequalities.
This paper analyzes the convergence and escape dynamics of Stochastic Gradient Descent in one-dimensional landscapes, establishing that while SGD reliably converges to local minima, it may linger near local maxima depending on noise variance and geometry, with specific results provided for the probability of escaping sharp maxima to neighboring minima.
This paper analyzes the overall net profits of two players in a "first to reach " game governed by an urn model, demonstrating that the statistical properties of the game's outcomes differ drastically across three distinct regimes involving sampling without replacement, sampling with replacement plus reinforcement, and a third unspecified regime.
This paper refines moment comparison inequalities for sums of random vectors uniformly distributed on Euclidean spheres by establishing sharp constants and introducing an optimal deficit term, particularly in high dimensions.
This paper establishes Gaussian approximation bounds for the finite-dimensional distributions of deep neural networks with randomly initialized weights and Lipschitz activations, proving convergence to a Gaussian limit as layer widths grow and deriving specific convergence rates that depend on the network depth.