Fractional Fick's law for the boundary driven exclusion process with long jumps

zbMath1364.60129arXiv1603.01234MaRDI QIDQ5346033

Cédric Bernardin, Byron Jiménez-Oviedo

Publication date: 8 June 2017

Full work available at URL: https://arxiv.org/abs/1603.01234

zbMATH Keywords

superdiffusionfractional diffusionFick's lawexclusion process with long jumps

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Interacting particle systems in time-dependent statistical mechanics (82C22) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Fractional partial differential equations (35R11)

Related Items (5)

Hydrostatic limit for the symmetric exclusion process with long jumps: supper-diffusive case ⋮ Hydrodynamic limit for a boundary driven super-diffusive symmetric exclusion ⋮ A microscopic model for a one parameter class of fractional Laplacians with Dirichlet boundary conditions ⋮ Equilibrium fluctuations for diffusive symmetric exclusion with long jumps and infinitely extended reservoirs ⋮ Non-equilibrium stationary properties of the boundary driven zero-range process with long jumps

Cites Work

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• 3/4-fractional superdiffusion in a system of harmonic oscillators perturbed by a conservative noise
• Occupation times of long-range exclusion and connections to KPZ class exponents
• Hitchhiker's guide to the fractional Sobolev spaces
• Hydrodynamics of stationary non-equilibrium states for some stochastic lattice gas models
• Interaction of Markov processes
• Macroscopic properties of a stationary non-equilibrium distribution for a non-gradient interacting particle system
• Nonlinear fluctuating hydrodynamics for anharmonic chains
• Recent progress in the theory of nonlinear diffusion with fractional Laplacian operators
• From normal diffusion to superdiffusion of energy in the evanescent flip noise limit
• Superdiffusion of energy in a chain of harmonic oscillators with noise
• Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains
• Hydrodynamical limit for a nongradient system: The generalized symmetric exclusion process
• Nonequilibrium scaling limit for a tagged particle in the simple exclusion process with long jumps
• A stochastic model of anomalous heat transport: analytical solution of the steady state
• On microscopic derivation of a fractional stochastic Burgers equation

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