281 papers
This paper provides a simple proof of the FKG inequality for random interlacements on transient weighted graphs and establishes 0-1 laws for non-local events, including a general result for increasing non-local events without additional assumptions.
This paper establishes finite-horizon mean-square strong and weak error bounds for Euler--Maruyama simulations of current-based leaky integrate-and-fire networks by employing a path-space pruning-and-balance strategy that accounts for the unique concentration of numerical error at stochastic threshold-crossing events.
This paper proposes a novel sampling method for unnormalized Boltzmann densities that leverages a sequence of Langevin samplers to efficiently simulate a probability flow ODE derived from linear stochastic interpolants by generating intermediate samples and robustly estimating the velocity field, while providing theoretical convergence guarantees and demonstrating effectiveness on challenging multimodal distributions and Bayesian inference tasks.
This paper proves that for sufficiently large , the uniform probability measures on three specific families of spanning subgraphs of the complete graph —namely connected spanning subgraphs, forests with exactly components, and connected spanning subgraphs with excess —satisfy the pairwise negative correlation property.
This paper establishes the first central limit theorems for the number of edges and unimodular triangulation edges in symmetric edge polytopes generated by Erdős–Rényi random graphs in high dimensions, utilizing the discrete Malliavin–Stein method to derive precise asymptotics and identify an atypical fluctuation regime where variance cancellation occurs.
This paper establishes the universality of high-dimensional spectral behavior and statistical limits for asymmetric rank-one spiked tensor models with non-Gaussian noise, demonstrating that the maximum-likelihood estimator's performance matches the Gaussian case under finite fourth-moment assumptions.
This paper investigates a Pearson diffusion process to demonstrate that while its noise-free limit exhibits rate-induced tipping where solutions escape a bounded domain in finite time, the presence of noise accelerates this escape.
This paper establishes a new existence theory for equilibria in continuous-time time-inconsistent stochastic control problems by proving that solutions to entropy-regularized exploratory equilibrium HJB equations converge to a weak solution of the generalized equilibrium HJB equation as the regularization vanishes, thereby resolving the open problem of existence without requiring strong regularity assumptions.
This paper establishes large- asymptotic upper and lower bounds for the annealed survival probability of a polymer moving in a medium of Poisson traps, proving that the decay rate is exponential with an exponent proportional to for any fixed time .
This paper investigates the selection of optimal two-block partitions to accelerate Markov chain mixing by establishing theoretical connections between KL divergence and Frobenius distance objectives and their respective decay rates, while proposing computationally feasible approximation algorithms to solve the resulting combinatorial optimization problem.
This paper provides a rigorous probabilistic construction of the massless Sinh-Gordon model on an infinite cylinder using Gaussian multiplicative chaos and spectral analysis, establishing the existence of discrete spectrum and a strictly positive ground state for the associated quantum operator while deriving scaling relations for its correlation functions.
This paper provides a quantitative large-deviations theory for the "catapult phase" in stochastic gradient descent training of shallow networks under NTK scaling, establishing an explicit criterion based on a function that determines whether large NTK-flattening spikes occur with high probability or decay rapidly depending on the learning rate, data, and kernel.
This paper introduces Stochastic Port-Hamiltonian Neural Networks (SPH-NNs), a framework that parameterizes Hamiltonian systems with neural networks to enforce physical passivity and skew-symmetry constraints, thereby achieving universal approximation of stochastic dynamics with guaranteed energy stability and superior long-term performance compared to standard baselines.
This paper demonstrates that a class of optimized e-value combinations remains valid even when tuning parameters are data-dependent, extending this result to a new category of "simultaneous e-variables" and proposing an improved combination test based on elementary symmetric polynomials.
This paper solves Merton's portfolio optimization problem in a multivariate fake stationary affine Volterra setting by employing a martingale optimality principle and a Riccati backward stochastic differential equation to derive semi-closed form optimal strategies, overcoming the challenges posed by non-Markovian and non-semimartingale dynamics.
This paper establishes Hoeffding-type concentration inequalities for sums of exchangeable random variables that exhibit anti-symmetry and provide tail bounds relative to the extreme means within the de Finetti mixing measure's support, thereby bridging the gap between finite sample and population means.
This paper establishes the first universality-breaking frontier in shuffle privacy by characterizing the asymptotic behavior of concentrated local randomizers that fail classical Gaussian limits, proving convergence to explicit Poisson, Skellam, and compound-Poisson shift experiments and providing a complete three-regime picture of shuffle privacy limits.
This paper investigates a once-reinforced random walk on the half-line and establishes the limiting behaviors for all moments of its range.
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 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.