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Volumn 6, Issue 2, 2004, Pages 207-276

On the zero-temperature or vanishing viscosity limit for certain markov processes arising from lagrangian dynamics

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EID: 2442509621     PISSN: 14359855     EISSN: None     Source Type: Journal    
DOI: 10.4171/JEMS/9     Document Type: Article
Times cited : (31)

References (36)
  • 1
    • 84990553776 scopus 로고
    • Brownian motion and Harnack inequality for Schrödinger operators
    • [AS82], Zbl 0459.60069 MR 84a:35062
    • [AS82] Aizenman, M., Simon, B.: Brownian motion and Harnack inequality for Schrödinger operators. Comm. Pure Appl. Math. 35, 209-273 (1982) Zbl 0459.60069 MR 84a:35062
    • (1982) Comm. Pure Appl. Math. , vol.35 , pp. 209-273
    • Aizenman, M.1    Simon, B.2
  • 2
    • 0002946916 scopus 로고
    • Equivalence of uniform hyperbolicity for symplectic twist maps and phonon gap for Frenkel-Kontorova models
    • [AMB92], Zbl 0802.58021 MR 93e:58144
    • [AMB92] Aubry, S., McKay, R. S., Baesens, C.: Equivalence of uniform hyperbolicity for symplectic twist maps and phonon gap for Frenkel-Kontorova models. Physica D 56, 123-134 (1992) Zbl 0802.58021 MR 93e:58144
    • (1992) Physica D , vol.56 , pp. 123-134
    • Aubry, S.1    McKay, R.S.2    Baesens, C.3
  • 3
    • 0003267441 scopus 로고
    • Solutions de viscosité des équations de Hamilton-Jacobi
    • [Ba94]. Springer, Zbl 0819.35002 MR 2000b:49054
    • [Ba94] Barles, G.: Solutions de viscosité des équations de Hamilton-Jacobi. Mathématiques et Applications 17, Springer (1994) Zbl 0819.35002 MR 2000b:49054
    • (1994) Mathématiques et Applications , vol.17
    • Barles, G.1
  • 4
    • 0001579803 scopus 로고
    • Méthodes de Laplace et de la phase stationnaire sur l'espace de Wiener
    • [Be88]. Zbl 0666.60026 MR 91h:60070
    • [Be88] Ben Arous, G.: Méthodes de Laplace et de la phase stationnaire sur l'espace de Wiener. Stochastics 25, 125-153 (1988) Zbl 0666.60026 MR 91h:60070
    • (1988) Stochastics , vol.25 , pp. 125-153
    • Ben Arous, G.1
  • 5
    • 0039666567 scopus 로고
    • Precise asymptotics in large deviations
    • [BDS93], Zbl 0791.60017 MR 93m:60052
    • [BDS93] Ben Arous, G., Deuschel, J. D., Stroock, D.W.: Precise asymptotics in large deviations. Bull. Sci. Math. 117, 107-124 (1993) Zbl 0791.60017 MR 93m:60052
    • (1993) Bull. Sci. Math. , vol.117 , pp. 107-124
    • Ben Arous, G.1    Deuschel, J.D.2    Stroock, D.W.3
  • 6
    • 0037829671 scopus 로고    scopus 로고
    • Connecting orbits of time dependent Lagrangian systems
    • [Ber02], Zbl 1008.37035 MR 2003m:37088
    • [Ber02] Bernard, P.: Connecting orbits of time dependent Lagrangian systems. Ann. Inst. Fourier (Grenoble) 52, 1533-1568 (2002) Zbl 1008.37035 MR 2003m:37088
    • (2002) Ann. Inst. Fourier (Grenoble) , vol.52 , pp. 1533-1568
    • Bernard, P.1
  • 7
    • 0038270743 scopus 로고    scopus 로고
    • Aubry-mather theory and hamilton-jacobi equations
    • [Bes02], Zbl pre01964925 MR 1974512
    • [Bes02] Bessi, U.: Aubry-Mather theory and Hamilton-Jacobi equations. Comm. Math. Phys. 235, 495-511 (2003) Zbl pre01964925 MR 1974512
    • (2003) Comm. Math. Phys. , vol.235 , pp. 495-511
    • Bessi, U.1
  • 8
    • 0033441520 scopus 로고    scopus 로고
    • Déterminants et intégrales de Fresnel. Symposium à la Mémoire de François Jaeger (Grenoble, 1998)
    • [CV99], Zbl 0920.35042 MR 2001k:58065
    • [CV99] Colin de Verdière, Y.: Déterminants et intégrales de Fresnel. Symposium à la Mémoire de François Jaeger (Grenoble, 1998), Ann. Inst. Fourier (Grenoble) 49, 861-881 (1999) Zbl 0920.35042 MR 2001k:58065
    • (1999) Ann. Inst. Fourier (Grenoble) , vol.49 , pp. 861-881
    • Colin de Verdière, Y.1
  • 9
    • 0040971816 scopus 로고    scopus 로고
    • Lyapunov minimizing measures for expanding maps of the circle
    • [CLT01], Zbl 0997.37016 MR 2002i:37038
    • [CLT01] Contreras, G., Lopes, A., Thieullen, P.: Lyapunov minimizing measures for expanding maps of the circle. Ergodic Theory Dynam. Systems 21, 1379-1409 (2001) Zbl 0997.37016 MR 2002i:37038
    • (2001) Ergodic Theory Dynam. Systems , vol.21 , pp. 1379-1409
    • Contreras, G.1    Lopes, A.2    Thieullen, P.3
  • 10
    • 0003620605 scopus 로고
    • [Co65]. Cambridge Univ. Press, Zbl 0123.26001 MR 29 #6234
    • [Co65] Copson, E. T.: Asymptotic Expansions. Cambridge Univ. Press (1965) Zbl 0123.26001 MR 29 #6234
    • (1965) Asymptotic Expansions
    • Copson, E.T.1
  • 11
    • 84968507121 scopus 로고
    • Some properties of viscosity solutions of Hamilton-Jacobi equations
    • [CEL84], Zbl 0543.35011 MR86a:35031
    • [CEL84] Crandall, M. G., Evans, L. C., Lions, P.-L.: Some properties of viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 282, 487-502 (1984) Zbl 0543.35011 MR86a:35031
    • (1984) Trans. Amer. Math. Soc. , vol.282 , pp. 487-502
    • Crandall, M.G.1    Evans, L.C.2    Lions, P.-L.3
  • 12
    • 84967758647 scopus 로고
    • Viscosity solutions of Hamilton-Jacobi equations
    • [CL83], Zbl 0599.35024 MR 85g:35029
    • [CL83] Crandall, M. G., Lions, P.-L.: Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 277, 1-42 (1983) Zbl 0599.35024 MR 85g:35029
    • (1983) Trans. Amer. Math. Soc. , vol.277 , pp. 1-42
    • Crandall, M.G.1    Lions, P.-L.2
  • 14
    • 0004121117 scopus 로고
    • [D168]. Hermann, Paris Zbl 0155.10001 MR 37 #255
    • [D168] Dieudonné, J.: Calcul infinitésimal. Hermann, Paris (1968) Zbl 0155.10001 MR 37 #255
    • (1968) Calcul Infinitésimal
    • Dieudonné, J.1
  • 16
    • 0031138612 scopus 로고    scopus 로고
    • Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens
    • [Fa97-1], Zbl 0885.58022 MR 98g:58151
    • [Fa97-1] Fathi, A.: Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens. C. R. Acad. Sci. Paris Sér. I Math. 324, 1043-1046 (1997) Zbl 0885.58022 MR 98g:58151
    • (1997) C. R. Acad. Sci. Paris Sér. I Math. , vol.324 , pp. 1043-1046
    • Fathi, A.1
  • 17
    • 0031231828 scopus 로고    scopus 로고
    • Solutions KAM faibles conjuguées et barrières de Peierls
    • [Fa97-2], Zbl 0943.37031 MR 99b:58209
    • [Fa97-2] Fathi, A.: Solutions KAM faibles conjuguées et barrières de Peierls. C. R. Acad. Sci. Paris Sér. I Math. 325, 649-652 (1997) Zbl 0943.37031 MR 99b:58209
    • (1997) C. R. Acad. Sci. Paris Sér. I Math. , vol.325 , pp. 649-652
    • Fathi, A.1
  • 18
    • 0041471525 scopus 로고    scopus 로고
    • A stochastic analog of Aubry-Mather theory
    • [Go02], Zbl pre01802917 MR 2003b:37096
    • [Go02] Gomes, D. A.: A stochastic analog of Aubry-Mather theory. Nonlinearity 15, 581-603 (2002) Zbl pre01802917 MR 2003b:37096
    • (2002) Nonlinearity , vol.15 , pp. 581-603
    • Gomes, D.A.1
  • 19
    • 0347554475 scopus 로고
    • Gibbs' functional on subshifts
    • [Ha90], Zbl 0711.58009 MR 92b:58128
    • [Ha90] Haydn, N. T. A.: Gibbs' functional on subshifts. Comm. Math. Phys. 134, 217-236 (1990) Zbl 0711.58009 MR 92b:58128
    • (1990) Comm. Math. Phys. , vol.134 , pp. 217-236
    • Haydn, N.T.A.1
  • 20
    • 0003195540 scopus 로고
    • Introduction to the modem theory of dynamical systems
    • [KH95], Cambridge Univ. Press, Zbl 0878.58020 MR 96c:58055
    • [KH95] Katok, A. B., Hasselblatt, B.: Introduction to the Modem Theory of Dynamical Systems. Encyclopedia Math. Appl. 54, Cambridge Univ. Press (1995) Zbl 0878.58020 MR 96c:58055
    • (1995) Encyclopedia Math. Appl. , vol.54
    • Katok, A.B.1    Hasselblatt, B.2
  • 21
    • 0003278519 scopus 로고
    • Semi-classical analysis for the schrödinger operator and applications
    • [He88], Springer, Berlin Zbl 0647.35002 MR 90c:81043
    • [He88] Helffer, B.: Semi-classical Analysis for the Schrödinger Operator and Applications. Lecture Notes in Math. 1336, Springer, Berlin (1988) Zbl 0647.35002 MR 90c:81043
    • (1988) Lecture Notes in Math. , vol.1336
    • Helffer, B.1
  • 22
    • 0001159401 scopus 로고
    • Subadditive ergodic theory
    • [Ki73], Zbl 0311.60018 MR 50 #8663
    • [Ki73] Kingman, J. F. C.: Subadditive ergodic theory. Ann. Probab. 1, 883-909 (1973) Zbl 0311.60018 MR 50 #8663
    • (1973) Ann. Probab. , vol.1 , pp. 883-909
    • Kingman, J.F.C.1
  • 23
    • 0003225839 scopus 로고
    • Gaussian measures in banach spaces
    • [Ku75], Springer, Zbl 0306.28010 MR 57 #1628
    • [Ku75] Kuo, H. H.: Gaussian Measures in Banach Spaces. Lecture Notes in Math. 463, Springer (1975) Zbl 0306.28010 MR 57 #1628
    • (1975) Lecture Notes in Math. , vol.463
    • Kuo, H.H.1
  • 24
    • 84966209310 scopus 로고
    • A theorem on infinite products of eigenvalues of Sturm-Liouville type operators
    • [LS65], Zbl 0374.34016 MR 56 #16040
    • [LS65] Levit, S., Smilansky, U.: A theorem on infinite products of eigenvalues of Sturm-Liouville type operators. Proc. Amer. Math. Soc. 65, 299-302 (1977) Zbl 0374.34016 MR 56 #16040
    • (1977) Proc. Amer. Math. Soc. , vol.65 , pp. 299-302
    • Levit, S.1    Smilansky, U.2
  • 25
    • 0013128343 scopus 로고
    • On the minimizing measures of Lagrangian dynamical systems
    • [Mn92], Zbl 0799.58030 MR 93h:58059
    • [Mn92] Mañé, R.: On the minimizing measures of Lagrangian dynamical systems. Nonlinearity 5, 623-638 (1992) Zbl 0799.58030 MR 93h:58059
    • (1992) Nonlinearity , vol.5 , pp. 623-638
    • Mañé, R.1
  • 26
    • 0000514824 scopus 로고    scopus 로고
    • Generic properties and problems of minimizing measures of Lagrangian systems
    • [Mn96], 273-310, Zbl 0886.58037 MR 97d:58118
    • [Mn96] Mañé, R.: Generic properties and problems of minimizing measures of Lagrangian systems. Nonlinearity 9, 273-310 (1996) Zbl 0886.58037 MR 97d:58118
    • (1996) Nonlinearity , vol.9
    • Mañé, R.1
  • 27
    • 0000793436 scopus 로고    scopus 로고
    • Lagrangian flows: The dynamics of globally minimizing orbits
    • [Mn97] Int. Cong. on Dyn. Syst.in Montevideo, F. Ledrappier et al. (eds.), Zbl 0870.58026 MR 98g:58059
    • [Mn97] Mañé, R.: Lagrangian flows: the dynamics of globally minimizing orbits. In: Int. Cong. on Dyn. Syst. in Montevideo, F. Ledrappier et al. (eds.), Pitman Res. Notes Math. 362, 120-131 (1996) Zbl 0870.58026 MR 98g:58059 Reprinted in Bol. Soc. Bras. Mat. 28, 141-153(1997) Zbl 0892.58064 MR 981:58092
    • (1996) Pitman Res. Notes Math. , vol.362 , pp. 120-131
    • Mañé, R.1
  • 28
    • 27144482772 scopus 로고    scopus 로고
    • Zbl 0892.58064 MR 981:58092
    • [Mn97] Mañé, R.: Lagrangian flows: the dynamics of globally minimizing orbits. In: Int. Cong. on Dyn. Syst. in Montevideo, F. Ledrappier et al. (eds.), Pitman Res. Notes Math. 362, 120-131 (1996) Zbl 0870.58026 MR 98g:58059 Reprinted in Bol. Soc. Bras. Mat. 28, 141-153(1997) Zbl 0892.58064 MR 981:58092
    • (1997) Bol. Soc. Bras. Mat. , vol.28 , pp. 141-153
  • 31
    • 84968484534 scopus 로고
    • Some asymptotic formulas for Wiener integrals
    • [Sc66], Zbl 0156.37602 MR 34 #1770
    • [Sc66] Schilder, M.: Some asymptotic formulas for Wiener integrals. Trans. Amer. Math. Soc. 125, 63-85 (1966) Zbl 0156.37602 MR 34 #1770
    • (1966) Trans. Amer. Math. Soc. , vol.125 , pp. 63-85
    • Schilder, M.1
  • 33
    • 0040218870 scopus 로고
    • Commensurate-incommensurate phase transitions in one-dimensional chains
    • [Si82], MR 84g:82012
    • [Si82] Sinai, Ya. G.: Commensurate-incommensurate phase transitions in one-dimensional chains. J. Statist. Phys. 29, 401-425 (1982) MR 84g:82012
    • (1982) J. Statist. Phys. , vol.29 , pp. 401-425
    • Sinai, Ya.G.1
  • 34
    • 33751098368 scopus 로고
    • Two results concerning asymptotic behavior of solutions of the Burgers equation with force
    • [Si91], Zbl 0978.35500 MR 92d:35261
    • [Si91] Sinai, Ya. G.: Two results concerning asymptotic behavior of solutions of the Burgers equation with force. J. Statist. Phys. 64, 1-12 (1991) Zbl 0978.35500 MR 92d:35261
    • (1991) J. Statist. Phys. , vol.64 , pp. 1-12
    • Sinai, Ya.G.1
  • 35
    • 0009289430 scopus 로고
    • A relation between the density of states and range of localization for one dimensional random systems
    • [Th72]
    • [Th72] Thouless, D. J.: A relation between the density of states and range of localization for one dimensional random systems. J. Phys. C: Solid State Phys. 5, 77-81 (1972)
    • (1972) J. Phys. C: Solid State Phys. , vol.5 , pp. 77-81
    • Thouless, D.J.1
  • 36
    • 84981761482 scopus 로고
    • Diffusion processes in small time intervals
    • [Va67], Zbl 0278.60051 MR 36 #970
    • [Va67] Varadhan, S.R.S.: Diffusion processes in small time intervals. Comm. Pure Appl. Math. 20, 659-685 (1967) Zbl 0278.60051 MR 36 #970
    • (1967) Comm. Pure Appl. Math. , vol.20 , pp. 659-685
    • Varadhan, S.R.S.1


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