Duality and hidden symmetries in interacting particle systems

Abstract

In the context of Markov processes, both in discrete and continuous setting, we show a general relation between duality functions and symmetries of the generator. If the generator can be written in the form of a Hamiltonian of a quantum spin system, then the "hidden" symmetries are easily derived. We illustrate our approach in processes of symmetric exclusion type, in which the symmetry is of SU(2) type, as well as for the Kipnis-Marchioro-Presutti (KMP) model for which we unveil its SU(1,1) symmetry. The KMP model is in turn an instantaneous thermalization limit of the energy process associated to a large family of models of interacting diffusions, which we call Brownian energy process (BEP) and which all possess the SU(1,1) symmetry. We treat in details the case where the system is in contact with reservoirs and the dual process becomes absorbing.

38 pages

References in corpus (4)

• Partially Asymmetric Exclusion Process with Open Boundaries
• Duality and exact correlations for a model of heat conduction
• On U_q(SU(2))-symmetric Driven Diffusion
• Fourier law in a momentum-conserving chain

Cited by in corpus (90)

• Mapping out of equilibrium into equilibrium in one-dimensional transport models
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• Dynamics of condensation in the symmetric inclusion process
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• Random loop representations for quantum spin systems
• Metastability in the reversible inclusion process
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• Self-Duality for the Two-Component Asymmetric Simple Exclusion Process
• Asymmetric stochastic transport models with ${\mathcal{U}}_q(\mathfrak{su}(1,1))$ symmetry
• An algebraic construction of duality functions for the stochastic U_q(A_n^{(1)}) vertex model and its degenerations
• Dynamics of condensation in the totally asymmetric inclusion process
• Langevin equations for reaction-diffusion processes
• A Multi-species ASEP(q,j) and q-TAZRP with Stochastic Duality
• Non-compact quantum spin chains as integrable stochastic particle processes
• Large Deviations in Stochastic Heat-Conduction Processes Provide a Gradient-Flow Structure for Heat Conduction
• Duality and hidden equilibrium in transport models
• Spectral form factor in a minimal bosonic model of many-body quantum chaos
• Duality in interacting particle systems and boson representation
• Orthogonal stochastic duality functions from Lie algebra representations
• Orthogonal Dualities of Markov Processes and Unitary Symmetries
• Self-duality of Markov processes and intertwining functions
• Integrable Floquet dynamics, generalized exclusion processes and "fused" matrix ansatz
• A reverse duality for the ASEP with open boundaries
• Hydrodynamics for the partial exclusion process in random environment
• Switching interacting particle systems: scaling limits, uphill diffusion and boundary layer
• Extended duality relations between birth-death processes and partial differential equations
• Symmetric inclusion process with slow boundary: hydrodynamics and hydrostatics
• The kinetic exclusion process: a tale of two fields
• Hydrodynamic limit of boundary driven exclusion processes with nonreversible boundary dynamics
• Duality and stationary distributions of the "Immediate Exchange Model" and its generalizations
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• On dualities for SSEP and ASEP with open boundary conditions
• Integrable stochastic dualities and the deformed Knizhnik-Zamolodchikov equation
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• Explosive condensation in symmetric mass transport models
• Monotonicity and Condensation in Homogeneous Stochastic Particle Systems
• Integrable heat conduction model
• On the notion(s) of duality for Markov processes
• Duality in stochastic processes from the viewpoint of basis expansions
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• Rare event simulation for stochastic dynamics in continuous time
• Approximate filtering via discrete dual processes
• Weakly Non-Equilibrium Properties of Symmetric Inclusion Process with Open Boundaries
• A generalized Asymmetric Exclusion Process with $U_q({\mathfrak{sl}}_2)$ stochastic duality
• Ergodic theory of multi-layer interacting particle systems
• Markov duality and Bethe ansatz formula for half-line open ASEP
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• Weak coupling limits in a stochastic model of heat conduction
• Spatially Inhomogeneous Populations with Seed-banks: Duality, Existence and Clustering
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• Supersymmetries in non-equilibrium Langevin dynamics
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• Mixing of the Averaging process and its discrete dual on finite-dimensional geometries
• Making Birth-Death Processes from Backward Fokker-Planck Equations for Computing Expectations in Langevin Systems
• Stochastic duality and eigenfunctions
• Zero range and finite range processes with asymmetric rate functions
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• Conservative interacting particles system with anomalous rate of ergodicity
• Orthogonal Intertwiners for Infinite Particle Systems in The Continuum
• Nonlinear Kalman filter based on duality relations between continuous and discrete-state stochastic processes
• Numerical methods to evaluate Koopman matrix from system equations
• Stationary states in infinite volume with non zero current
• Heat conduction and the nonequilibrium stationary states of stochastic energy exchange processes
• Equilibrium perturbations for stochastic interacting systems
• Symmetry classes of classical stochastic processes
• Second Time Scale of the Metastability of Reversible Inclusion Processes
• Coupling independent walkers and the inclusion process
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• Lecture notes on large deviations in non-equilibrium diffusive systems
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• Generalized immediate exchange models and their symmetries
• Hydrodynamic limit for a $d$-dimensional open symmetric exclusion process
• Intertwinings for Continuum Particle Systems: an Algebraic Approach
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