Asymmetric stochastic transport models with \(\mathcal{U}_q(\mathfrak{su}(1,1))\) symmetry

DOI10.1007/s10955-016-1473-4zbMath1353.82049arXiv1507.01478OpenAlexW2963999632WikidataQ59469552 ScholiaQ59469552MaRDI QIDQ300700

Tomohiro Sasamoto, Frank Redig, Cristian Giardinà, Gioia Carinci

Publication date: 28 June 2016

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.01478

zbMATH Keywords

Hamiltonian dynamics\({\mathcal{U}}_q(\mathfrak{su}(1,1))\) quantum Lie algebraasymmetric transport modelsasymmetric version of the IP( ASIP)duality and self-duality relationsexactly solvable stochastic systemsinclusion process (IP)Kipnis-Marchioro-Presutti (KMP) modelMarkov processes with an algebraic structuresymmetric and asymmetric exclusion processes

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Interacting particle systems in time-dependent statistical mechanics (82C22) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Diffusion processes (60J60) Applications of Lie (super)algebras to physics, etc. (17B81) Transport processes in time-dependent statistical mechanics (82C70) Quantum groups (quantized function algebras) and their representations (20G42) Functional limit theorems; invariance principles (60F17) Multiplicative functionals and Markov processes (60J57) Stochastic (Schramm-)Loewner evolution (SLE) (60J67)

Related Items (19)

Local thermal equilibrium for certain stochastic models of heat transport ⋮ Local equilibrium in inhomogeneous stochastic models of heat transport ⋮ Ergodic theory of the symmetric inclusion process ⋮ \(\operatorname{ASEP}(q,j)\) converges to the KPZ equation ⋮ A generalized asymmetric exclusion process with \(U_q(\mathfrak {sl}_2)\) stochastic duality ⋮ Exact formulas for two interacting particles and applications in particle systems with duality ⋮ Totally asymmetric limit for models of heat conduction ⋮ Orthogonal polynomial duality of a two-species asymmetric exclusion process ⋮ Explicit central elements of \(U_q(\mathfrak{gl}(N+1))\) ⋮ Duality for a boundary driven asymmetric model of energy transport ⋮ Unnamed Item ⋮ Stochastic Duality and Orthogonal Polynomials ⋮ Heat conduction and the nonequilibrium stationary states of stochastic energy exchange processes ⋮ \(q\)-orthogonal dualities for asymmetric particle systems ⋮ An algebraic construction of duality functions for the stochastic \(\mathcal U_q(A_n^{(1)})\) vertex model and its degenerations ⋮ Distribution of a tagged particle position in the one-dimensional symmetric simple exclusion process with two-sided Bernoulli initial condition ⋮ Self-duality of Markov processes and intertwining functions ⋮ Duality Relations for the Periodic ASEP Conditioned on a Low Current ⋮ Orthogonal dualities of Markov processes and unitary symmetries

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