@incollection{AST_2003__287__71_0, author = {Fern\'andez, Roberto and Toom, Andr\'e}, title = {Non-Gibbsianness of the invariant measures of non-reversible cellular automata with totally asymmetric noise}, booktitle = {Geometric methods in dynamics (II) : Volume in honor of Jacob Palis}, editor = {de Melo, Wellington and Viana, Marcelo and Yoccoz, Jean-Christophe}, series = {Ast\'erisque}, pages = {71--87}, publisher = {Soci\'et\'e math\'ematique de France}, number = {287}, year = {2003}, mrnumber = {2040001}, zbl = {1140.82327}, language = {en}, url = {http://archive.numdam.org/item/AST_2003__287__71_0/} }
TY - CHAP AU - Fernández, Roberto AU - Toom, André TI - Non-Gibbsianness of the invariant measures of non-reversible cellular automata with totally asymmetric noise BT - Geometric methods in dynamics (II) : Volume in honor of Jacob Palis AU - Collectif ED - de Melo, Wellington ED - Viana, Marcelo ED - Yoccoz, Jean-Christophe T3 - Astérisque PY - 2003 SP - 71 EP - 87 IS - 287 PB - Société mathématique de France UR - http://archive.numdam.org/item/AST_2003__287__71_0/ LA - en ID - AST_2003__287__71_0 ER -
%0 Book Section %A Fernández, Roberto %A Toom, André %T Non-Gibbsianness of the invariant measures of non-reversible cellular automata with totally asymmetric noise %B Geometric methods in dynamics (II) : Volume in honor of Jacob Palis %A Collectif %E de Melo, Wellington %E Viana, Marcelo %E Yoccoz, Jean-Christophe %S Astérisque %D 2003 %P 71-87 %N 287 %I Société mathématique de France %U http://archive.numdam.org/item/AST_2003__287__71_0/ %G en %F AST_2003__287__71_0
Fernández, Roberto; Toom, André. Non-Gibbsianness of the invariant measures of non-reversible cellular automata with totally asymmetric noise, dans Geometric methods in dynamics (II) : Volume in honor of Jacob Palis, Astérisque, no. 287 (2003), pp. 71-87. http://archive.numdam.org/item/AST_2003__287__71_0/
[1] Role of Irreversibility in Stabilizing Complex and Nonergodic Behavior in Locally Interacting Discrete Systems. Phys. Rev. Letters, v. 55 (1985), n. 7, pp. 657-660. | DOI
and .[2] A useful renormalization argument. In Random walks, Brownlan motion, and interacting particle systems, 113-152, Birkhäuser Boston, Boston, MA, 1991. | DOI | MR | Zbl
and .[3] Renormalization group pathologies and the definition of Gibbs states. Comm. Math. Phys., 194(2): 359-388, 1998. | DOI | MR | Zbl
, , and .[4] The renormalization-group peculiarities of Griffiths and Pearce: What have we learned ? In Mathematical Results in Statistical Mechanics, S. Miracle-Sole, J. Ruiz and V. Zagrebnov eds., World Scientific, Singapore. 1999, pp. 509-26. | MR | Zbl
.[5] Non-Gibbsian limit for large-block majority-spin transformations. J. Stat. Phys., 55:171-181, 1989. | DOI | MR | Zbl
and .[6] Regularity properties and pathologies of position-space renormalization-group transformations: Scope and limitations of Gibbsian theory. J. Stat. Phys., 72:879-1167, 1993. | DOI | MR | Zbl
, , and .[7] Robustness of the non-Gibbsian property: some examples. J. Phys. A, 29:2465-73, 1996. | DOI | MR | Zbl
and .[8] Dobrushin's program on Gibbsianity restoration: weakly Gibbs and almost Gibbs random fields. In On Dobrushin's way. From probability theory to statistical physics, Amer. Math. Soc., Providence, RI, 2000, pp. 59-70. | MR | Zbl
, , and .[9] (Almost) Gibbsian description of the sign fields of fields. J. Statist Phys., 92:353-368, 1998. | DOI | MR | Zbl
and .[10] Random fields in lattices. The Gibbsianness issue. Resenhas, 3(4):391-421, 1998. | MR | Zbl
.[11] Measures for lattice systems. Phys. A, 263 (1-4): 117-130, 1999. | DOI | MR
.Measures for lattice systems. STAT-PHYS 20 (Paris, 1998).
.[12] Gibbs Measures and Phase Transitions. Walter de Gruyter (de Gruyter Studies in Mathematics, Vol. 9), Berlin-New York, 1988. | MR | Zbl
.[13] Gibbs description of a system of random variables. Probl. Inform. Transmission, 10:258-65, 1974. | MR | Zbl
.[14] The effect of an external field on an interface, entropic repulsion, J. Stat. Phys., v. 46, pp. 39-49, 1987. | DOI | MR
and ,[15] Statistical mechanics of probabilistic cellular automata. J. Stat. Phys., 59:117-70, 1990. | DOI | MR | Zbl
, , and .[16] Pseudo-free energies and large deviations for non-Gibbsian FKG measures. Prob. Th. Rel Fields, 77:49-64, 1988. | DOI | MR | Zbl
and .[17] Non-Gibbsianness of the reduced -measure, Stoch. Proc. Appl., v. 74, pp. 83-88, 1998. | DOI | MR | Zbl
,[18] Weakly Gibbsian measures for lattice spin systems. J. Statist. Phys., 89 (3-4): 561-579, 1997. | DOI | MR | Zbl
and .[19] The interaction potential of a stationary measure of a high-noise spinflip process. J. Math. Phys., 34:3030-1, 1993. | DOI | MR | Zbl
and .[20] The (non-)Gibbsian nature of states invariant under stochastic transformations. Physica A, 206:587-603, 1994. | DOI
and .[21] Gibbsian versus non-Gibbsian nature of stationary states for Toom probabilistic cellular automata via simulations. Phys. Rev. E, 55:6582-8, 1997. | DOI
.[22] Stationary states of Toom cellular automata in simulations. Phys. Rev. E, 60:3787-95, 1999. | DOI
.[23] A simple stochastic cluster dynamics: rigorous results. J. Phys. A, 24:3135-57, 1991. | DOI | MR
and .[24] Modelling of voting with random errors. Automatics and telemechanics, v. 10, pp. 103-107, 1969 (in Russian). | Zbl
, and .[25] Thermodynamical aspects of classical lattice systems. Preprint. Notes for a minicourse at the IV-th Brazilian School of Probability, Mambucaba, Brazil, August 2000. | MR | Zbl
.[26] Convex Analysis. Princeton University Press, Princeton, 1970. | DOI | MR | Zbl
.[27] On invariant measures in non-ergodic random media. In Probabilistic Methods of Investigation, A. Kolmogorov, editor, Moscow University Press, Moscow, 1972, pp. 43-51. (In Russian).
.[28] Nonergodic multidimensional systems of automata. Probl. Inform. Transmission, 10(3):70-79, 1974. | MR | Zbl
.[29] Stable and attractive trajectories in multicomponent systems. In Multicomponent Random Systems. Advances in Probability and Related Topics, R. Dobrushin and Ya. Sinai eds., Dekker, New York, 1980, v. 6, pp. 549-576. | MR | Zbl
.[30] On the question of quasilocality in large systems of locally interacting components. K. U. Leuven thesis, 1995. | MR
.