메뉴 건너뛰기




Volumn 32, Issue 2, 2004, Pages 1691-1726

Relative entropy and variational properties of generalized Gibbsian measures

Author keywords

Disordered systems; Generalized Gibbs measures; Gibbs versus non Gibbs; Morita approach; Random field Ising model; Renormalization group; Variational principle

Indexed keywords


EID: 18144445935     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/009117904000000342     Document Type: Article
Times cited : (33)

References (32)
  • 1
    • 0000178537 scopus 로고
    • A rigorous renormalization group method for interfaces in random media
    • BOVIER, A. and KÜLSKE, C. (1994). A rigorous renormalization group method for interfaces in random media. Rev. Math. Phys. 6 413-496.
    • (1994) Rev. Math. Phys. , vol.6 , pp. 413-496
    • Bovier, A.1    Külske, C.2
  • 2
    • 0000702675 scopus 로고
    • Phase transition in the 3d random field Ising model
    • BRICMONT, J. and KUPIAINEN, A. (1988). Phase transition in the 3d random field Ising model. Comm. Math. Phys. 142 539-572.
    • (1988) Comm. Math. Phys. , vol.142 , pp. 539-572
    • Bricmont, J.1    Kupiainen, A.2
  • 3
    • 0032094628 scopus 로고    scopus 로고
    • Renormalization group pathologies and the definition of Gibbs states
    • BRICMONT, J., KUPIAINEN, A. and LEFEVERE, R. (1998). Renormalization group pathologies and the definition of Gibbs states. Comm. Math. Phys. 194 359-388.
    • (1998) Comm. Math. Phys. , vol.194 , pp. 359-388
    • Bricmont, J.1    Kupiainen, A.2    Lefevere, R.3
  • 4
    • 0031515867 scopus 로고    scopus 로고
    • Gibbsian description of "non Gibbsian" field
    • DOBRUSHIN, R. L. and SHLOSMAN, S. B. (1997). Gibbsian description of "non Gibbsian" field. Russian Math. Surveys 52 285-297. [Also see "Non Gibbsian" states and their description. Comm. Math. Phys. 200 (1999) 125-179.]
    • (1997) Russian Math. Surveys , vol.52 , pp. 285-297
    • Dobrushin, R.L.1    Shlosman, S.B.2
  • 5
    • 0033466556 scopus 로고    scopus 로고
    • "Non Gibbsian" states and their description
    • DOBRUSHIN, R. L. and SHLOSMAN, S. B. (1997). Gibbsian description of "non Gibbsian" field. Russian Math. Surveys 52 285-297. [Also see "Non Gibbsian" states and their description. Comm. Math. Phys. 200 (1999) 125-179.]
    • (1999) Comm. Math. Phys. , vol.200 , pp. 125-179
  • 6
    • 0346041559 scopus 로고    scopus 로고
    • Variational principle and almost quasilocality for renormalized measures
    • FERNÁNDEZ, R., LE NY, A. and REDIG, F. (2002). Variational principle and almost quasilocality for renormalized measures. J. Statist. Phys. 111 465-477.
    • (2002) J. Statist. Phys. , vol.111 , pp. 465-477
    • Fernández, R.1    Le Ny, A.2    Redig, F.3
  • 7
    • 0039644940 scopus 로고    scopus 로고
    • Global specifications and non-quasilocality of projections of Gibbs measures
    • FERNÁNDEZ, R. and PFISTER, C.-E. (1997). Global specifications and non-quasilocality of projections of Gibbs measures. Ann. Probab. 25 1284-1315.
    • (1997) Ann. Probab. , vol.25 , pp. 1284-1315
    • Fernández, R.1    Pfister, C.-E.2
  • 9
    • 0642265805 scopus 로고
    • Mathematical properties of position-space renormalization-group transformations
    • GRIFFITHS, R. B. and PEARCE, P. A. (1979). Mathematical properties of position-space renormalization-group transformations. J. Statist. Phys. 20 499-545.
    • (1979) J. Statist. Phys. , vol.20 , pp. 499-545
    • Griffiths, R.B.1    Pearce, P.A.2
  • 11
    • 0016078912 scopus 로고
    • Gibbs description of a system of random variables
    • KOZLOV, O. K. (1974). Gibbs description of a system of random variables. Problems Inform. Transmission 10 258-265.
    • (1974) Problems Inform. Transmission , vol.10 , pp. 258-265
    • Kozlov, O.K.1
  • 12
    • 4243259994 scopus 로고
    • Critical behavior of the randomly spin diluted 2D Ising model: A grand ensemble approach
    • KÜHN, R. and MAZZEO, G. (1994). Critical behavior of the randomly spin diluted 2D Ising model: A grand ensemble approach. Phys. Rev. Lett. 73 2268-2271.
    • (1994) Phys. Rev. Lett. , vol.73 , pp. 2268-2271
    • Kühn, R.1    Mazzeo, G.2
  • 13
    • 85035295687 scopus 로고    scopus 로고
    • Reply to "Comment on 'Critical behavior of the randomly spin diluted 2D Ising model: A grand ensemble approach'."
    • KÜHN, R. and MAZZEO, G. (2000). Reply to "Comment on 'Critical behavior of the randomly spin diluted 2D Ising model: A grand ensemble approach'." Phys. Rev. Lett. 84 6135.
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 6135
    • Kühn, R.1    Mazzeo, G.2
  • 14
    • 0007131312 scopus 로고    scopus 로고
    • (Non-)Gibbsianness and phase transitions in random lattice spin models
    • KÜLSKE, C. (1999). (Non-)Gibbsianness and phase transitions in random lattice spin models. Markov Processes and Related Fields 5 357-383.
    • (1999) Markov Processes and Related Fields , vol.5 , pp. 357-383
    • Külske, C.1
  • 15
    • 0035624973 scopus 로고    scopus 로고
    • Weakly Gibbsian representation for joint measures of quenched lattice spin models
    • KÜLSKE, C. (2001). Weakly Gibbsian representation for joint measures of quenched lattice spin models. Probab. Theory Related Fields 119 1-30.
    • (2001) Probab. Theory Related Fields , vol.119 , pp. 1-30
    • Külske, C.1
  • 16
    • 85088669604 scopus 로고    scopus 로고
    • Almost and weak Gibbsianness: A long-range pair-interaction example
    • LEFEVERE, R. (1999). Almost and weak Gibbsianness: A long-range pair-interaction example. J. Statist. Phys. 96 109-113.
    • (1999) J. Statist. Phys. , vol.96 , pp. 109-113
    • Lefevere, R.1
  • 17
    • 85088669708 scopus 로고    scopus 로고
    • Variational principle for some renormalized measures
    • LEFEVERE, R. (1999). Variational principle for some renormalized measures. J. Statist. Phys. 95 785-803.
    • (1999) J. Statist. Phys. , vol.95 , pp. 785-803
    • Lefevere, R.1
  • 18
    • 0034340702 scopus 로고    scopus 로고
    • Percolation, path large deviations and weak Gibbsianity
    • MAES, C., REDIG, F., SHLOSMAN, S. and VAN MOFFAERT, A. (2000). Percolation, path large deviations and weak Gibbsianity. Comm. Math. Phys. 209 517-545.
    • (2000) Comm. Math. Phys. , vol.209 , pp. 517-545
    • Maes, C.1    Redig, F.2    Shlosman, S.3    Van Moffaert, A.4
  • 21
    • 0033245919 scopus 로고    scopus 로고
    • The restriction of the Ising model to a layer
    • MAES, C., REDIG, F. and VAN MOFFAERT, A. (1999). The restriction of the Ising model to a Layer. J. Statist. Phys. 96 69-107.
    • (1999) J. Statist. Phys. , vol.96 , pp. 69-107
    • Maes, C.1    Redig, F.2    Van Moffaert, A.3
  • 22
    • 0001028722 scopus 로고    scopus 로고
    • Relative energies for non-Gibbsian states
    • MAES, C. and VANDE VELDE, K. (1997). Relative energies for non-Gibbsian states. Comm. Math. Phys. 189 277-286.
    • (1997) Comm. Math. Phys. , vol.189 , pp. 277-286
    • Maes, C.1    Vande Velde, K.2
  • 23
    • 0242373810 scopus 로고
    • Statistical mechanics of quenched solid solutions with application to magnetically dilute alloys
    • MORITA, T. (1964). Statistical mechanics of quenched solid solutions with application to magnetically dilute alloys. J. Math. Phys. 5 1402-1405.
    • (1964) J. Math. Phys. , vol.5 , pp. 1402-1405
    • Morita, T.1
  • 24
    • 0141507622 scopus 로고    scopus 로고
    • Thermodynamical aspects of classical lattice systems
    • (V. Sidoravicius, ed.) Birkhaüser, Boston
    • PFISTER, C.-E. (2002). Thermodynamical aspects of classical lattice systems. In In and Out of Equilibrium. Probability with a Physical Flavour (V. Sidoravicius, ed.) 393-472. Birkhaüser, Boston.
    • (2002) In and Out of Equilibrium. Probability with a Physical Flavour , pp. 393-472
    • Pfister, C.-E.1
  • 25
    • 3042522385 scopus 로고
    • A strong variational principle for continuous spin systems
    • PIRLOT, M. (1980). A strong variational principle for continuous spin systems. J. Appl. Probab. 17 47-58.
    • (1980) J. Appl. Probab. , vol.17 , pp. 47-58
    • Pirlot, M.1
  • 26
    • 21844525446 scopus 로고
    • Entropy, limit theorems, and variational principles for disordered lattice systems
    • SEPPÄLÄINEN, T. (1995). Entropy, limit theorems, and variational principles for disordered lattice systems. Comm. Math. Phys. 171 233-277.
    • (1995) Comm. Math. Phys. , vol.171 , pp. 233-277
    • Seppäläinen, T.1
  • 27
    • 0001964043 scopus 로고
    • Potentials for almost Markovian random fields
    • SULLIVAN, W. G. (1973). Potentials for almost Markovian random fields. Comm. Math. Phys. 3361-74.
    • (1973) Comm. Math. Phys. , pp. 3361-3374
    • Sullivan, W.G.1
  • 28
    • 0036002928 scopus 로고    scopus 로고
    • Possible loss and recovery of Gibbsianness during the stochastic evolution of Gibbs measures
    • VAN ENTER, A. C. D., FERNÁNDEZ, R., DEN HOLLANDER, F. and REDIG, F. (2002). Possible loss and recovery of Gibbsianness during the stochastic evolution of Gibbs measures. Comm. Math. Phys. 226 101-130.
    • (2002) Comm. Math. Phys. , vol.226 , pp. 101-130
    • Van Enter, A.C.D.1    Fernández, R.2    Den Hollander, F.3    Redig, F.4
  • 29
    • 34250084304 scopus 로고
    • Regularity properties and pathologies of position-space renormalization-group transformations: Scope and limitations of Gibbsian theory
    • VAN ENTER, A. C. D., FERNÁNDEZ, R. and SOKAL, A. D. (1993). Regularity properties and pathologies of position-space renormalization-group transformations: Scope and limitations of Gibbsian theory. J. Statist. Phys. 72 879-1167.
    • (1993) J. Statist. Phys. , vol.72 , pp. 879-1167
    • Van Enter, A.C.D.1    Fernández, R.2    Sokal, A.D.3
  • 30
    • 84856124590 scopus 로고    scopus 로고
    • Comment on "Critical behavior of the randomly spin diluted 2D Ising model: A grand ensemble approach"
    • VAN ENTER, A. C. D., MAES, C. and KÜLSKE, C. (2000). Comment on "Critical behavior of the randomly spin diluted 2D Ising model: A grand ensemble approach". Phys. Rev. Lett. 84 6134.
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 6134
    • Van Enter, A.C.D.1    Maes, C.2    Külske, C.3
  • 32
    • 0032396538 scopus 로고    scopus 로고
    • An ergodic process of zero divergence distance from the class of all stationary processes
    • XU, S. (1997). An ergodic process of zero divergence distance from the class of all stationary processes. J. Theoret. Probab. 11 181-196.
    • (1997) J. Theoret. Probab. , vol.11 , pp. 181-196
    • Xu, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.