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.
Lectures on Dimers
4 Pith papers cite this work. Polarity classification is still indexing.
4
Pith papers citing it
abstract
These are lecture notes for lectures at the Park City Math Institute, summer 2007. We cover aspects of the dimer model on planar, periodic bipartite graphs, including local statistics, limit shapes and fluctuations.
representative citing papers
Proves convergence in law of random 3D dimer flows to the unique entropy-maximizing divergence-free flow and establishes corresponding large deviation principles.
Establishes that traces of q-deformed higher continued fraction matrices equal dimer partition functions on good higher dimers of band graphs and proves lattice structure plus palindromic symmetry for certain families.
citing papers explorer
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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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Large deviations for the 3D dimer model
Proves convergence in law of random 3D dimer flows to the unique entropy-maximizing divergence-free flow and establishes corresponding large deviation principles.
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Higher $q$-Continued Fractions and Dimers on Band Graphs
Establishes that traces of q-deformed higher continued fraction matrices equal dimer partition functions on good higher dimers of band graphs and proves lattice structure plus palindromic symmetry for certain families.