Actas de congresos
Microscopic Structure Of The K-step Exclusion Process
Registro en:
Bulletin Of The Brazilian Mathematical Society. , v. 33, n. 3, p. 319 - 339, 2002.
1003569
2-s2.0-0036880371
Autor
Freire M.V.
Guiol H.
Ravishankar K.
Saada E.
Institución
Resumen
We review the hydrodynamics and discuss the shock, rarefaction fan and contact discontinuity at a microscopic level for a one-dimensional totally asymmetric k-step exclusion process. In particular we define a microscopical object that identifies the shock in the decreasing case. 33 3 319 339 Bahadoran, C., Guiol, H., Ravishankar, K., Saada, E., A constructive approach to Euler hydrodynamics for attractive processes. Application to k-step exclusion (2002) Stoc. Process. Appl., 99 (1), pp. 1-30 Doornik, J.A., (1999) Object-Oriented Matrix Programming Using Ox, 3rd Ed., , http://www.nuff.ox.ac.uk/users/doornik, London: Timberlake Consultants Press and Oxford Durrett, R., Ten lectures on particle systems (1993) Lecture Notes in Math., 1608, pp. 97-201. , Lectures on probability theory (Saint-Flour), Springer, Berlin Ferrari, P.A., The simple exclusion process as seen from a tagged particle (1986) Ann. Probab., 14 (4), pp. 1277-1290 Ferrari, P.A., Shocks in the Burgers equation and the asymmetric simple exclusion process (1990) Math. Appl., 75, pp. 25-64. , Statistical physics, automata networks and dynamical systems (Santiago), Kluwer Acad. Publ., Dordrecht Ferrari, P.A., Limit theorems for tagged particles (1995) Markov Process. Related Fields, 2 (1), pp. 17-40. , Disordered systems and statistical physics: rigorous results (Budapest) Ferrari, P.A., Fontes, L.R.G., Shock fluctuations in the asymmetric simple exclusion process (1994) Probab. Theory Related Fields, 99 (2), pp. 305-319 Ferrari, P.A., Kipnis, C., Second class particles in the rarefaction fan (1995) Ann. Inst. H. Poincaré Probab. Statist., 31 (1), pp. 143-154 Guiol, H., Some properties of k-step exclusion processes (1999) J. Statist. Phys., 94 (3-4), pp. 495-511 Harris, T.E., Nearest neighbor Markov interaction processes on multidimensional lattices (1972) Adv. in Math., 9, pp. 66-89 Liggett, T.M., Long-range exclusion processes (1980) Ann. Probab., 8 (5), pp. 861-889 Liggett, T.M., Interacting particle systems (1985) Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 276, pp. xv+488. , Springer-Verlag, New York Liggett, T.M., Stochastic interacting systems: Contact, voter and exclusion processes (1999) Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 324, pp. xii+332. , Springer-Verlag, Berlin Seppäläinen, T., A variational coupling for a totally asymmetric exclusion process with long jumps but no passing (1998) Fields Inst. Commun., 27, pp. 117-130. , Hydrodynamic limits and related topics (Toronto, ON), Amer. Math. Soc., Providence, RI