Open Access
Issue
ESAIM: PS
Volume 24, 2020
Page(s) 526 - 580
DOI https://doi.org/10.1051/ps/2020008
Published online 09 October 2020
  1. W.W. Adams and P. Loustaunau, An introduction to Gröbner bases, in Vol. 3 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI (1994). [CrossRef] [Google Scholar]
  2. E.D. Andjel, Invariant measures for the zero range processes. Ann. Probab. 10 (1982) 525–547. [Google Scholar]
  3. O. Angel, The stationary measure of a 2-type totally asymmetric exclusion process. J. Combin. Theory Ser. A 113 (2006) 4. [CrossRef] [Google Scholar]
  4. M. Balázs, F. Rassoul-Agha, T. Seppäläinen and S. Sethuraman, Existence of the zero range process and a deposition model with superlinear growth rates. Ann. Probab. 35 (2007) 1201–1249. [Google Scholar]
  5. R.A. Blythe and M.R. Evans, Nonequilibrium steady states of matrix-product form: a solver’s guide. J. Phys. A 40 (2007) R333–R441. [CrossRef] [Google Scholar]
  6. O. Cappé, E. Moulines and T. Rydén, Inference in hidden Markov models. Springer Science & Business Media, Berlin (2006). [Google Scholar]
  7. J. Casse and J.-F. Marckert, Markovianity of the invariant distribution of probabilistic cellular automata on the line. Stoch. Process Appl. 125 (2015) 3458–3483. [CrossRef] [Google Scholar]
  8. N. Crampe, E. Ragoucy and M. Vanicat, Integrable approach to simple exclusion processes with boundaries. Review and progress. J. Stat. Mech. Theory Exp. 11 (2014) P11032. [CrossRef] [Google Scholar]
  9. P. Dai Pra, P. Louis and S. Roelly, Stationary Measures and Phase Transition for a Class of Probabilistic Cellular Automata. ESAIM: PS 6 (2002) 89–104. [CrossRef] [EDP Sciences] [Google Scholar]
  10. B. Derrida, M.R. Evans, V. Hakim and V. Pasquier, Exact solution of a 1D asymmetric exclusion model using a matrix formulation. J. Phys. A 26 (1993) 1493–1517. [CrossRef] [MathSciNet] [Google Scholar]
  11. Z.-J. Ding, Z.-Y. Gao, J. Long, Y.-B. Xie, J.-X. Ding, X. Ling, R. Kühne and Q. Shi. Phase transition in 2d partially asymmetric simple exclusion process with two species. J. Stat. Mech. Theory Exp. 2014 (2014) P10002. [CrossRef] [Google Scholar]
  12. M.R. Evans, S.N. Majumdar and R.K.P. Zia, Factorized steady states in mass transport models. J. Phys. A 37 (2004) L275–L280. [CrossRef] [Google Scholar]
  13. L. Fajfrová, T. Gobron and E. Saada, Invariant measures of mass migration processes. Electron. J. Probab. 21 (2016) 60. [Google Scholar]
  14. J.-C. Faugère, Personal page. Available from: https://www-polsys.lip6.fr/~jcf/ (2020). [Google Scholar]
  15. L. Fredes and J.-F. Marckert, Maple file and pdf file. Available at: http://www.labri.fr/perso/marckert/Grobner.mw, http://www.labri.fr/perso/marckert/Grobner.pdf (2020). [Google Scholar]
  16. H-O. Georgii, Gibbs Measures and Phase Transitions, Series:De Gruyter Studies in Mathematics 9, De Gruyter, Berlin (2011). [CrossRef] [Google Scholar]
  17. R.L. Greenblatt and J.L. Lebowitz, Product measure steady states of generalized zero range processes. J. Phys. A 39 (2006) 1565–1573. [CrossRef] [Google Scholar]
  18. T.E. Harris, Nearest-neighbor Markov interaction processes on multidimensional lattices. Adv. Math. 9 (1972) 66–89. [CrossRef] [Google Scholar]
  19. C. Kipnis and C. Landim, Scaling limits of interacting particle systems, Vol. 320 of Fundamental Principles of Mathematical Sciences. Springer-Verlag, Berlin (1999). [Google Scholar]
  20. R. Kraaij, Stationary product measures for conservative particle systems and ergodicity criteria. Electron. J. Probab. 18 (2013) 88. [Google Scholar]
  21. T.M. Liggett, Interacting particle systems, Classics in Mathematics. Springer-Verlag, Berlin (2005). [CrossRef] [Google Scholar]
  22. J. Mairesse and I. Marcovici, Probabilistic cellular automata and random fields with iid directions. Ann. Inst. Henri Poincaré Probab. Stat. 50 (2014) 455–475. [CrossRef] [Google Scholar]
  23. J.M. Swart, A Course in Interacting Particle Systems (2017). [Google Scholar]
  24. A. Toom, N. Vasilyev, O. Stavskaya, L. Mityushin, G. Kurdyumov and S. Pirogov, Stochastic cellular systems: ergodicity, memory, morphogenesis (Part: Discrete local Markov systems. Manchester University Press, Manchester (1990), 1–182. [Google Scholar]
  25. N.B. Vasilyev, Bernoulli and Markov stationary measures in discrete local interactions, Vol. 1 of Developments in Statistics. Academic Press, New York (1978). [Google Scholar]
  26. N.B. Vasilyev and O.K. Kozlov, Reversible Markov chains with local interactions. Adv. Probab. Related Topics 6 (1980) 451–469. [Google Scholar]

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