TASEP hydrodynamics using microscopic characteristics

The convergence of the totally asymmetric simple exclusion process to the solution of the Burgers equation is a classical result. In his seminal 1981 paper, Herman Rost proved the convergence of the density fields and local equilibrium when the limiting solution of the equation is a rarefaction fan....

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Publicado: 2018
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Totally asymmetric simple exclusion process
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15495787_v15_n_p1_Ferrari
http://hdl.handle.net/20.500.12110/paper_15495787_v15_n_p1_Ferrari
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_15495787_v15_n_p1_Ferrari
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spelling paper:paper_15495787_v15_n_p1_Ferrari2023-06-08T16:21:21Z TASEP hydrodynamics using microscopic characteristics Totally asymmetric simple exclusion process The convergence of the totally asymmetric simple exclusion process to the solution of the Burgers equation is a classical result. In his seminal 1981 paper, Herman Rost proved the convergence of the density fields and local equilibrium when the limiting solution of the equation is a rarefaction fan. An important tool of his proof is the subadditive ergodic theorem. We prove his results by showing how second class particles transport the rarefaction-fan solution, as characteristics do for the Burgers equation, avoiding subadditivity. Along the way we show laws of large numbers for tagged particles, fluxes and second class particles, and simplify existing proofs in the shock cases. The presentation is self contained. © 2017, Probability Surveys. 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15495787_v15_n_p1_Ferrari http://hdl.handle.net/20.500.12110/paper_15495787_v15_n_p1_Ferrari
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Totally asymmetric simple exclusion process
spellingShingle Totally asymmetric simple exclusion process
TASEP hydrodynamics using microscopic characteristics
topic_facet Totally asymmetric simple exclusion process
description The convergence of the totally asymmetric simple exclusion process to the solution of the Burgers equation is a classical result. In his seminal 1981 paper, Herman Rost proved the convergence of the density fields and local equilibrium when the limiting solution of the equation is a rarefaction fan. An important tool of his proof is the subadditive ergodic theorem. We prove his results by showing how second class particles transport the rarefaction-fan solution, as characteristics do for the Burgers equation, avoiding subadditivity. Along the way we show laws of large numbers for tagged particles, fluxes and second class particles, and simplify existing proofs in the shock cases. The presentation is self contained. © 2017, Probability Surveys.
title TASEP hydrodynamics using microscopic characteristics
title_short TASEP hydrodynamics using microscopic characteristics
title_full TASEP hydrodynamics using microscopic characteristics
title_fullStr TASEP hydrodynamics using microscopic characteristics
title_full_unstemmed TASEP hydrodynamics using microscopic characteristics
title_sort tasep hydrodynamics using microscopic characteristics
publishDate 2018
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15495787_v15_n_p1_Ferrari
http://hdl.handle.net/20.500.12110/paper_15495787_v15_n_p1_Ferrari
_version_ 1768542195127681024

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