Empirical measures from Kac's particle system converge to the Boltzmann equation solution for very soft potentials, proving propagation of chaos for all kernel classes.
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New theoretical results on estimators and intervals for predicting unseen outcomes in additional samples from discrete distributions, with extensions to grouped incidence data.
The symmetric Dyson exclusion process exhibits ballistic scaling and non-local hydrodynamics with current j[ρ] = (1/π) sin(πρ) sinh(π H ρ) where H is the Hilbert transform, equivalent to a local two-field system, with exact solutions for block initial states matching simulations.
Hydrodynamic limit of symmetric exclusion process on Poisson graphs approximating weighted Riemannian manifolds and principal bundles is a Fokker-Planck equation.
Authors review double-limit problems in singular perturbation theory and propose a three-step process to partition parameter space near singular limits and identify asymptotic problems for unification.
A literature review synthesizing developments in quantum Wasserstein distances, their applications, and unresolved questions.
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Propagation of chaos for the Boltzmann equation with very soft potentials
Empirical measures from Kac's particle system converge to the Boltzmann equation solution for very soft potentials, proving propagation of chaos for all kernel classes.
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The Unseen Species Problem Revisited
New theoretical results on estimators and intervals for predicting unseen outcomes in additional samples from discrete distributions, with extensions to grouped incidence data.
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Emergent Hydrodynamics in an Exclusion Process with Long-Range Interactions
The symmetric Dyson exclusion process exhibits ballistic scaling and non-local hydrodynamics with current j[ρ] = (1/π) sin(πρ) sinh(π H ρ) where H is the Hilbert transform, equivalent to a local two-field system, with exact solutions for block initial states matching simulations.
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Hydrodynamic limit of the symmetric exclusion process on complete Riemannian manifolds and principal bundles
Hydrodynamic limit of symmetric exclusion process on Poisson graphs approximating weighted Riemannian manifolds and principal bundles is a Fokker-Planck equation.
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A General View on Double Limits in Differential Equations
Authors review double-limit problems in singular perturbation theory and propose a three-step process to partition parameter space near singular limits and identify asymptotic problems for unification.
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Wasserstein Distances on Quantum Structures: an Overview
A literature review synthesizing developments in quantum Wasserstein distances, their applications, and unresolved questions.