295 papers
This paper establishes a necessary and sufficient condition for the existence of an equivalent measurable version of a stochastic process on arbitrary probability spaces by characterizing measurability with respect to a specific -algebra larger than the product -algebra, thereby generalizing previous results on separable versions and liftings.
This paper establishes the existence, uniqueness, and exponential mixing of an invariant measure for a stochastic generalized Constantin-Lax-Majda-DeGregorio model of turbulence featuring an anomalous enstrophy cascade, utilizing the Krylov-Bogoliubov argument and large viscosity conditions to advance the dynamical systems understanding of turbulent cascades.
This paper establishes a precise asymptotic transfer mechanism for critical recursive composition schemes in map enumeration, demonstrating how singular structures and associated central limit theorems for statistics on 2-connected maps propagate to the broader class of all maps.
This paper introduces the Random Quadratic Form (RQF), a stochastic differential equation on a sphere that demonstrates how common noise induces synchronization and token clustering in deep transformers, offering an alternative explanation to self-attention for these phenomena.
This paper investigates the universal asymptotic behavior of correlations in two-dimensional Coulomb systems featuring an outpost Jordan curve, showing that these correlations along the outpost and outer boundary are governed by a reproducing kernel for a specific Hilbert space of analytic functions, thereby generalizing recent Szegő-type edge correlation results.
This paper establishes a Pontryagin-type stochastic maximum principle for optimal control of McKean-Vlasov stochastic partial differential equations with nonconvex control sets by employing spike variation methods and Lions derivatives within an infinite-dimensional framework.
This paper investigates the large deviations of subgraph counts in inhomogeneous random graphs with power-law degree distributions, establishing that rare events involving numerous subgraphs correspond to the emergence of extreme hubs and deriving sharp results for clique counts when the expected subgraph number is sublinear.
The paper proves that the height function of the six-vertex model on with spectral parameter converges to a full-plane Gaussian free field in the scaling limit, a result that extends to anisotropic weights via a suitable lattice embedding.
This paper establishes a large-deviation principle for the maximal energy of a spin glass with spins by deriving a Parisi-type formula for fractional moments and leveraging convex duality to show that the rate function is asymptotically quadratic near its minimum if and only if an external magnetic field is present.
This paper presents an optimization-based formulation of the Red Light Green Light (RLGL) algorithm for computing stationary distributions of large Markov chains via Dirichlet-energy minimization and coordinate descent, thereby clarifying its behavior, establishing exponential convergence for specific chain classes, and suggesting practical scheduling strategies to accelerate convergence.
This paper establishes the necessary and sufficient conditions under which a heavy-tailed random variable can be paired with an independent heavy-tailed variable such that their minimum results in a light-tailed distribution, characterizing the specific "segmented" structure required for this phenomenon.
This paper establishes the existence, uniqueness, and moment bounds for a generalized spatial model of Muller's ratchet with density-dependent rates and deleterious mutations, utilizing a sequence of approximating processes and a delicate coupling argument to overcome challenges posed by non-monotonicity and non-local interactions.
This paper establishes a functional law of large numbers for a spatial model of Muller's ratchet, proving that the system converges to an infinite system of partial differential equations that rigorously determine population spreading speeds and demonstrate that deleterious mutations can indeed surf deterministic population waves.
This paper establishes the convergence of the near-critical dimer model's height function to a massive sine-Gordon model by introducing a novel framework of discrete massive holomorphic functions with complex-valued, non-constant mass to derive exact discrete Cauchy–Riemann equations for the inverse Kasteleyn matrix.
This paper establishes that embedded infinite plane triangulations within ergodic scale-free environments converge to their circle packing and Riemann uniformization embeddings on a large scale, provided that specific moment and connectivity conditions are met.
This paper introduces and analyzes a broad class of continuous directed polymers in driven by Gaussian environments, establishing their structural properties, proving a sharp measure-theoretic dichotomy regarding their relation to Wiener measure, and demonstrating diffusive behavior in high dimensions and high temperatures, thereby extending the Alberts--Khanin--Quastel framework to higher-dimensional settings.
This paper establishes that faithful Bayesian networks constitute a dense, open, and typical set across various parametric and nonparametric classes, thereby providing a rigorous theoretical foundation for the consistency of constraint-based causal discovery algorithms like PC and FCI.
This paper proposes an arbitrage-free valuation framework for catastrophe stop-loss reinsurance contracts using a compound dynamic contagion process and the Esscher transform to price liabilities arising from both conventional and emerging risks like climate change, cyberattacks, and pandemics.
This paper introduces a nonparametric Weighted Random Dot Product Graph (WRDPG) model that extends traditional network analysis by using latent positions and moment-generating functions to capture higher-order edge weight distributions beyond the mean, while providing consistent estimation guarantees and a generative framework for sampling weighted graphs.
This paper establishes that Value-at-Risk (VaR) for non-negative random variables is strictly sub-additive only in the degenerate co-monotonic case, while providing a unified framework based on negative simplex dependence and simplex dominance to characterize conditions under which VaR becomes fully super-additive across all probability levels.