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Abstract:

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.

Registro:

Documento: Artículo
Título:TASEP hydrodynamics using microscopic characteristics
Autor:Ferrari, P.A.
Filiación:Universidad de Buenos Aires, IMAS CONICET, Argentina
Palabras clave:Totally asymmetric simple exclusion process
Año:2018
Volumen:15
Página de inicio:1
Página de fin:27
DOI: http://dx.doi.org/10.1214/17-PS284
Título revista:Probability Surveys
Título revista abreviado:Probab. Surv.
ISSN:15495787
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15495787_v15_n_p1_Ferrari

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Citas:

---------- APA ----------
(2018) . TASEP hydrodynamics using microscopic characteristics. Probability Surveys, 15, 1-27.
http://dx.doi.org/10.1214/17-PS284
---------- CHICAGO ----------
Ferrari, P.A. "TASEP hydrodynamics using microscopic characteristics" . Probability Surveys 15 (2018) : 1-27.
http://dx.doi.org/10.1214/17-PS284
---------- MLA ----------
Ferrari, P.A. "TASEP hydrodynamics using microscopic characteristics" . Probability Surveys, vol. 15, 2018, pp. 1-27.
http://dx.doi.org/10.1214/17-PS284
---------- VANCOUVER ----------
Ferrari, P.A. TASEP hydrodynamics using microscopic characteristics. Probab. Surv. 2018;15:1-27.
http://dx.doi.org/10.1214/17-PS284