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.
Interaction of Markov processes
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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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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.