INVESTIGADORES
FERRARI pablo Augusto
artículos
Título:
TASEP hydrodynamics using microscopic characteristics
Autor/es:
PABLO A. FERRARI
Revista:
Probability Surveys
Editorial:
Probability Surveys
Referencias:
Lugar: Oxford; Año: 2018 vol. 15 p. 1 - 27
ISSN:
1549-5787
Resumen:
The convergence of the totally asymmetric simple exclusionprocess to the solution of the Burgers equation is a classical result. In hisseminal 1981 paper, Herman Rost proved the convergence of the densityfields and local equilibrium when the limiting solution of the equation isa rarefaction fan. An important tool of his proof is the subadditive ergodictheorem. We prove his results by showing how second class particlestransport the rarefaction-fan solution, as characteristics do for the Burgersequation, avoiding subadditivity. Along the way we show laws of largenumbers for tagged particles, fluxes and second class particles, and simplifyexisting proofs in the shock cases. The presentation is self contained.
