Under multicritical conditions the edge scaling limit of correlations for the shifted Schur measure converges to the higher-order Airy kernel determinant, demonstrating a Pfaffian-to-determinantal transition.
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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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Multicritical Scaling Limit of Shifted Schur Measure
Under multicritical conditions the edge scaling limit of correlations for the shifted Schur measure converges to the higher-order Airy kernel determinant, demonstrating a Pfaffian-to-determinantal transition.
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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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