publication . Article . Preprint . Report . Other literature type . 2011

REGULAR G-MEASURES ARE NOT ALWAYS GIBBSIAN

Fernandez, Roberto; Gallo, Sandro; Maillard, Gregory;
Open Access English
Abstract
CNRS Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Made available in DSpace on 2014-08-01T18:32:16Z (GMT). No. of bitstreams: 0 Previous issue date: 2011 Made available in DSpace on 2015-11-26T17:02:11Z (GMT). No. of bitstreams: 2 WOS000297228500002.pdf: 136734 bytes, checksum: dcd0c95edc4394ca7e58fdcbcfc924ec (MD5) WOS000297228500002.pdf.txt: 23582 bytes, checksum: 1cff51d56113bf361c5c4881dd9efd2e (MD5) Previous issue date: 2011 Regular g-measures are discrete-time processes determined by conditional expectations with respect to the past. One-dimensional Gibbs measures, on the other hand, are fields determined by simu...
Subjects
free text keywords: $g$-measures, chains with variable-length memory, g-measures, Discrete-time stochastic processes, Mathematical Physics, non-Gibbsianness, Chains, 82B20, 37A05, 60G10, 82B20, 37A05, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], Mathematics - Probability, 60G10, chains with complete connections
17 references, page 1 of 2

[1] R. Bowen. Equilibrium states and the ergodic theory of Anosov di eomorphisms, Lecture Notes in Mathematics, Vol. 470, Springer-Verlag, Berlin, 1975.

[2] R. L. Dobrushin, The description of a random eld by means of conditional probabilities and conditions of its regularity. Theory Probab. Appl., 13 (1968) 197{224.

[3] A.C.D. van Enter, R. Fernandez, and A.D. Sokal, Regularity properties and pathologies of position-space renormalization-group transformations: scope and limitations of Gibbsian theory, J. Stat. Phys. 72 (1993) 879{1167. [OpenAIRE]

[4] A.C.D. van Enter and E. Verbitskiy, Erasure entropies and Gibbs measures, Markov Process. Related Fields 16 (2010) 3{14.

[5] R. Fernandez, Gibbsianness and non-Gibbsianness in Lattice random elds, In: Mathematical statistical physics, (A. Bovier, A.C.D. van Enter, F. den Hollander and F. Dunlop eds.), 731{799, Elsevier B. V., Amsterdam, 2006.

[6] R. Fernandez and G. Maillard, Chains with complete connections and one-dimensional Gibbs measures, Electron. J. Probab. 9 (2004) 145{176.

[7] R. Fernandez and G. Maillard, Construction of a speci cation from its singleton part, ALEA 2 (2006) 297{315. [OpenAIRE]

[8] S. Gallo, Chains with unbounded variable length memory: perfect simulation and visible regeneration scheme, To appear in Adv. in Appl. Probab.

[9] H.-O. Georgii, Gibbs Measures and Phase Transitions, de Gruyter Studies in Mathematics, Vol. 9, Walter de Gruyter & Co., Berlin, 1988.

[10] T. E. Harris, On chains of in nite order, Paci c J. Math., 5 (1955) 707{24. [OpenAIRE]

[11] S. Kalikow, Random Markov processes and uniform martingales, Isr. J. Math., 71 (1990) 33{54.

[12] M. Keane, Strongly mixing g-measures, Inventiones Math. 16 (1972) 309{324.

[13] G. Keller, Equilibrium states in ergodic theory, London Mathematical Society Student Texts, Vol. 42, Cambridge University Press, Cambridge, 1998.

[14] O. K. Kozlov, Gibbs description of a system of random variables, Probl. Inform. Transmission, 10 (1974) 258{265.

[15] O. E. Lanford III and D. Ruelle, Observables at in nity and states with short range correlations in statistical mechanics, Comm. Math. Phys., 13 (1969) 194{215.

17 references, page 1 of 2
Abstract
CNRS Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Made available in DSpace on 2014-08-01T18:32:16Z (GMT). No. of bitstreams: 0 Previous issue date: 2011 Made available in DSpace on 2015-11-26T17:02:11Z (GMT). No. of bitstreams: 2 WOS000297228500002.pdf: 136734 bytes, checksum: dcd0c95edc4394ca7e58fdcbcfc924ec (MD5) WOS000297228500002.pdf.txt: 23582 bytes, checksum: 1cff51d56113bf361c5c4881dd9efd2e (MD5) Previous issue date: 2011 Regular g-measures are discrete-time processes determined by conditional expectations with respect to the past. One-dimensional Gibbs measures, on the other hand, are fields determined by simu...
Subjects
free text keywords: $g$-measures, chains with variable-length memory, g-measures, Discrete-time stochastic processes, Mathematical Physics, non-Gibbsianness, Chains, 82B20, 37A05, 60G10, 82B20, 37A05, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], Mathematics - Probability, 60G10, chains with complete connections
17 references, page 1 of 2

[1] R. Bowen. Equilibrium states and the ergodic theory of Anosov di eomorphisms, Lecture Notes in Mathematics, Vol. 470, Springer-Verlag, Berlin, 1975.

[2] R. L. Dobrushin, The description of a random eld by means of conditional probabilities and conditions of its regularity. Theory Probab. Appl., 13 (1968) 197{224.

[3] A.C.D. van Enter, R. Fernandez, and A.D. Sokal, Regularity properties and pathologies of position-space renormalization-group transformations: scope and limitations of Gibbsian theory, J. Stat. Phys. 72 (1993) 879{1167. [OpenAIRE]

[4] A.C.D. van Enter and E. Verbitskiy, Erasure entropies and Gibbs measures, Markov Process. Related Fields 16 (2010) 3{14.

[5] R. Fernandez, Gibbsianness and non-Gibbsianness in Lattice random elds, In: Mathematical statistical physics, (A. Bovier, A.C.D. van Enter, F. den Hollander and F. Dunlop eds.), 731{799, Elsevier B. V., Amsterdam, 2006.

[6] R. Fernandez and G. Maillard, Chains with complete connections and one-dimensional Gibbs measures, Electron. J. Probab. 9 (2004) 145{176.

[7] R. Fernandez and G. Maillard, Construction of a speci cation from its singleton part, ALEA 2 (2006) 297{315. [OpenAIRE]

[8] S. Gallo, Chains with unbounded variable length memory: perfect simulation and visible regeneration scheme, To appear in Adv. in Appl. Probab.

[9] H.-O. Georgii, Gibbs Measures and Phase Transitions, de Gruyter Studies in Mathematics, Vol. 9, Walter de Gruyter & Co., Berlin, 1988.

[10] T. E. Harris, On chains of in nite order, Paci c J. Math., 5 (1955) 707{24. [OpenAIRE]

[11] S. Kalikow, Random Markov processes and uniform martingales, Isr. J. Math., 71 (1990) 33{54.

[12] M. Keane, Strongly mixing g-measures, Inventiones Math. 16 (1972) 309{324.

[13] G. Keller, Equilibrium states in ergodic theory, London Mathematical Society Student Texts, Vol. 42, Cambridge University Press, Cambridge, 1998.

[14] O. K. Kozlov, Gibbs description of a system of random variables, Probl. Inform. Transmission, 10 (1974) 258{265.

[15] O. E. Lanford III and D. Ruelle, Observables at in nity and states with short range correlations in statistical mechanics, Comm. Math. Phys., 13 (1969) 194{215.

17 references, page 1 of 2
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publication . Article . Preprint . Report . Other literature type . 2011

REGULAR G-MEASURES ARE NOT ALWAYS GIBBSIAN

Fernandez, Roberto; Gallo, Sandro; Maillard, Gregory;