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Volumn 137, Issue 1-2, 2007, Pages 121-160

N/V-limit for stochastic dynamics in continuous particle systems

Author keywords

Diffusion processes; Interacting particle systems; Limit theorems

Indexed keywords


EID: 33846888291     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-006-0499-y     Document Type: Review
Times cited : (11)

References (31)
  • 1
  • 2
    • 0001613648 scopus 로고    scopus 로고
    • Analysis and geometry on configuration spaces: The Gibbsian case
    • Albeverio, S., Kondratiev, Yu.G., Röckner, M.: Analysis and geometry on configuration spaces: The Gibbsian case. J. Funct. Anal. 157, 242-291 (1998)
    • (1998) J. Funct. Anal , vol.157 , pp. 242-291
    • Albeverio, S.1    Kondratiev, Y.G.2    Röckner, M.3
  • 3
    • 33846888823 scopus 로고
    • Mathematical description of the equilibrium state of classical systems on the basis of the canonical ensemble formalism
    • Bogolyubov, D., Petrina, D.Ya., Khatset, B.I.: Mathematical description of the equilibrium state of classical systems on the basis of the canonical ensemble formalism. Theo. Math. Phys. 1 (2), 194-212 (1970)
    • (1970) Theo. Math. Phys , vol.1 , Issue.2 , pp. 194-212
    • Bogolyubov, D.1    Petrina, D.Y.2    Khatset, B.I.3
  • 4
    • 0003535774 scopus 로고
    • Academic Press, London, New York
    • Choquet, G.: Topology. Academic Press, London, New York, 1966
    • (1966) Topology
    • Choquet, G.1
  • 5
    • 0009216028 scopus 로고
    • The existence and continuity of pressure in classical statistical physics
    • Dobrushin, R.L., Minlos, R.A.: The existence and continuity of pressure in classical statistical physics. Theory Prob. Appl. 12 (4), 535-559 (1967)
    • (1967) Theory Prob. Appl , vol.12 , Issue.4 , pp. 535-559
    • Dobrushin, R.L.1    Minlos, R.A.2
  • 6
    • 33846882409 scopus 로고    scopus 로고
    • Eberle, A.: Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators, 1718 of Lecture Notes in Mathematics. Springer, Berlin, Heidelberg, New York, 1999
    • Eberle, A.: Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators, 1718 of Lecture Notes in Mathematics. Springer, Berlin, Heidelberg, New York, 1999
  • 8
    • 33846856748 scopus 로고    scopus 로고
    • Constuction of diffusions with reflecting boundary condition and an application to continuous N-particle systems with singular interactions
    • Fattler, T., Grothaus, M.: Constuction of diffusions with reflecting boundary condition and an application to continuous N-particle systems with singular interactions. BiBoS preprint 04-12-170, Bielefeld University, 2004
    • (2004) BiBoS preprint 04-12-170, Bielefeld University
    • Fattler, T.1    Grothaus, M.2
  • 10
    • 0037933505 scopus 로고    scopus 로고
    • An infinite system of Brownian balls with infinite range interaction
    • Fradon, M., Roelly, S., Tanemura, H.: An infinite system of Brownian balls with infinite range interaction. Stochastic Process. Appl. 90 (1), 43-66 (2000)
    • (2000) Stochastic Process. Appl , vol.90 , Issue.1 , pp. 43-66
    • Fradon, M.1    Roelly, S.2    Tanemura, H.3
  • 11
    • 33846873699 scopus 로고    scopus 로고
    • Georgii, H.-O.: Canonical Gibbs Measures, 760 of Lecture Notes in Mathematics. Springer, Berlin, Heidelberg, New York, 1979
    • Georgii, H.-O.: Canonical Gibbs Measures, 760 of Lecture Notes in Mathematics. Springer, Berlin, Heidelberg, New York, 1979
  • 12
    • 21844497518 scopus 로고
    • The equivalence of ensembles for classical systems of particles
    • Georgii, H.-O.: The equivalence of ensembles for classical systems of particles. J. Stat. Phys. 80 (5/6), 1341-1378 (1995)
    • (1995) J. Stat. Phys , vol.80 , Issue.5-6 , pp. 1341-1378
    • Georgii, H.-O.1
  • 13
    • 0037696889 scopus 로고    scopus 로고
    • Scaling limit of stochastic dynamics in classical continuous systems
    • Grothaus, M., Kondratiev, Yu.G., Lytvynov, E., Röckner, M.: Scaling limit of stochastic dynamics in classical continuous systems. Ann. Prob. 31 (3), 1494-1532 (2003)
    • (2003) Ann. Prob , vol.31 , Issue.3 , pp. 1494-1532
    • Grothaus, M.1    Kondratiev, Y.G.2    Lytvynov, E.3    Röckner, M.4
  • 17
    • 29144468602 scopus 로고    scopus 로고
    • Mosco convergence of Dirichlet forms in infinite dimensions with changing reference measures
    • Kolesnikov, A.V.: Mosco convergence of Dirichlet forms in infinite dimensions with changing reference measures. J. Funct. Anal. 230 (2), 382-418 (2006)
    • (2006) J. Funct. Anal , vol.230 , Issue.2 , pp. 382-418
    • Kolesnikov, A.V.1
  • 18
    • 4043070671 scopus 로고    scopus 로고
    • Convergence of spectral structures: A functional analytic theory and its applications to spectral geometry
    • Kuwae, K., Shioya, T.: Convergence of spectral structures: A functional analytic theory and its applications to spectral geometry. Comm. Anal. Geom. 11 (4), 599-673 (2003)
    • (2003) Comm. Anal. Geom , vol.11 , Issue.4 , pp. 599-673
    • Kuwae, K.1    Shioya, T.2
  • 19
    • 0041114569 scopus 로고
    • Unendlichdimensionale Wienerprozesse mit Wechselwirkung II
    • Lang, R.: Unendlichdimensionale Wienerprozesse mit Wechselwirkung II. Z. Wahrsch. verw. Gebiete 39, 277-299 (1977)
    • (1977) Z. Wahrsch. verw. Gebiete , vol.39 , pp. 277-299
    • Lang, R.1
  • 20
    • 0001220564 scopus 로고
    • A crossing estimate for the canonical process on a Dirichlet space and a tightness result. Colloque Paul Lévy sur les processes stochastique
    • Lyons, T.J., Zheng, W.A.: A crossing estimate for the canonical process on a Dirichlet space and a tightness result. Colloque Paul Lévy sur les processes stochastique, Asterisque 157-158, 249-272 (1988)
    • (1988) Asterisque , vol.157-158 , pp. 249-272
    • Lyons, T.J.1    Zheng, W.A.2
  • 21
    • 0000362483 scopus 로고
    • Decomposition of Dirichlet processes and its applications
    • Lyons, T.J., Zhang, T.S.: Decomposition of Dirichlet processes and its applications. Ann. Prob. 22 (1), 494-524 (1994)
    • (1994) Ann. Prob , vol.22 , Issue.1 , pp. 494-524
    • Lyons, T.J.1    Zhang, T.S.2
  • 22
    • 0000548556 scopus 로고
    • Composite media and asymptotic Dirichlet forms
    • Mosco, U.: Composite media and asymptotic Dirichlet forms. J. Funct. Anal. 123 (2), 368-421 (1994)
    • (1994) J. Funct. Anal , vol.123 , Issue.2 , pp. 368-421
    • Mosco, U.1
  • 24
    • 0030526567 scopus 로고    scopus 로고
    • Dirichlet form approach to infinite-dimensional Wiener process with singular interactions
    • Osada, H.: Dirichlet form approach to infinite-dimensional Wiener process with singular interactions. Comm. Math. Phys. 176, 117-131 (1996)
    • (1996) Comm. Math. Phys , vol.176 , pp. 117-131
    • Osada, H.1
  • 26
    • 0001174680 scopus 로고
    • Superstable interactions in classical statistical mechanics
    • Ruelle, D.: Superstable interactions in classical statistical mechanics. Comm. Math. Phys. 18, 127-159 (1970)
    • (1970) Comm. Math. Phys , vol.18 , pp. 127-159
    • Ruelle, D.1
  • 27
    • 0013398075 scopus 로고
    • A remark on infinite-dimensional Wiener processes with interactions
    • Shiga, T.: A remark on infinite-dimensional Wiener processes with interactions. Z. Wahrsch. Verw. Gebiete 47 (3), 299-304 (1979)
    • (1979) Z. Wahrsch. Verw. Gebiete , vol.47 , Issue.3 , pp. 299-304
    • Shiga, T.1
  • 28
    • 0001986635 scopus 로고
    • Equilibrium fluctuations for interacting Brownian particles
    • Spohn, H.: Equilibrium fluctuations for interacting Brownian particles. Comm. Math. Phys. 103, 1-33 (1986)
    • (1986) Comm. Math. Phys , vol.103 , pp. 1-33
    • Spohn, H.1
  • 29
    • 0038515373 scopus 로고    scopus 로고
    • The maximum Markovian self-adjoint extension of Dirichlet operators for interacting particle systems
    • Schmuland, B., Sun, W.: The maximum Markovian self-adjoint extension of Dirichlet operators for interacting particle systems. Forum Math. 15 (4), 615-638 (2003)
    • (2003) Forum Math , vol.15 , Issue.4 , pp. 615-638
    • Schmuland, B.1    Sun, W.2
  • 31
    • 0000436663 scopus 로고    scopus 로고
    • Construction of infinite-dimensional interacting diffusion processes through Dirichlet forms
    • Yoshida, M.W.: Construction of infinite-dimensional interacting diffusion processes through Dirichlet forms. Prob. Theory Related Fields 106, 265-297 (1996)
    • (1996) Prob. Theory Related Fields , vol.106 , pp. 265-297
    • Yoshida, M.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.