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Volumn 131, Issue 6, 2008, Pages 1023-1038

Rare events in stochastic partial differential equations on large spatial domains

Author keywords

Large deviation theory; Metastability; Nucleation; Phase transformation; Rare events; Small noise; Spatially extended system; Stochastic partial differential equation

Indexed keywords


EID: 44349189777     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-008-9537-8     Document Type: Article
Times cited : (23)

References (50)
  • 1
    • 0033458290 scopus 로고    scopus 로고
    • Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem
    • Aldous, D., Diaconis, P.: Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem. Bull. Am. Math. Soc. 36, 413-432 (1999)
    • (1999) Bull. Am. Math. Soc , vol.36 , pp. 413-432
    • Aldous, D.1    Diaconis, P.2
  • 2
    • 33846588411 scopus 로고    scopus 로고
    • Testing transition state theory on Kac-Zwanzig model
    • Ariel, G., Vanden-Eijnden, E.: Testing transition state theory on Kac-Zwanzig model. J. Stat. Phys. 126, 43-73 (2007)
    • (2007) J. Stat. Phys , vol.126 , pp. 43-73
    • Ariel, G.1    Vanden-Eijnden, E.2
  • 3
    • 85204052956 scopus 로고
    • Über die Reaktiongeschwindkeit bei der inversion von Rohrzucker durch Säueren
    • Arrhenius, S.A.: Über die Reaktiongeschwindkeit bei der inversion von Rohrzucker durch Säueren. Z. Phys. Chemie 4 (1899)
    • (1899) Z. Phys. Chemie , vol.4
    • Arrhenius, S.A.1
  • 4
    • 0342869049 scopus 로고
    • Kinetics of phase change. I. General theory
    • Avrami, M.: Kinetics of phase change. I. General theory. J. Chem. Phys. 7, 1103-1122 (1939)
    • (1939) J. Chem. Phys , vol.7 , pp. 1103-1122
    • Avrami, M.1
  • 5
    • 0033443150 scopus 로고    scopus 로고
    • On the distribution of the length of the longest increasing subsequence of random permutations
    • Baik, J., Deift, P., Johansson, K.: On the distribution of the length of the longest increasing subsequence of random permutations. J. Am. Math. Soc. 12, 1119-1178 (1999)
    • (1999) J. Am. Math. Soc , vol.12 , pp. 1119-1178
    • Baik, J.1    Deift, P.2    Johansson, K.3
  • 7
    • 4644347796 scopus 로고    scopus 로고
    • Metastability in reversible diffusion processes. I. Sharp asymptotics for capacities and exit times
    • Bovier, A., Eckhoff, M., Gayrard, V., Klein, M.: Metastability in reversible diffusion processes. I. Sharp asymptotics for capacities and exit times. J. Eur. Math. Soc. 6, 399-424 (2004)
    • (2004) J. Eur. Math. Soc , vol.6 , pp. 399-424
    • Bovier, A.1    Eckhoff, M.2    Gayrard, V.3    Klein, M.4
  • 8
    • 0032271311 scopus 로고    scopus 로고
    • Interface fluctuations for the D=1 stochastic Ginzburg-Landau equation with nonsymmetric reaction term
    • Brassesco, S., Buttà, P.: Interface fluctuations for the D=1 stochastic Ginzburg-Landau equation with nonsymmetric reaction term. J. Stat. Phys. 93, 1111-1142 (1998)
    • (1998) J. Stat. Phys , vol.93 , pp. 1111-1142
    • Brassesco, S.1    Buttà, P.2
  • 9
    • 0002637757 scopus 로고
    • Brownian fluctuations of the interface in the D=1 Ginzburg-Landau equation with noise
    • Brassesco, S., De Masi, A., Presutti, E.: Brownian fluctuations of the interface in the D=1 Ginzburg-Landau equation with noise. Ann. Inst. Henri Poincaré 31, 81-118 (1995)
    • (1995) Ann. Inst. Henri Poincaré , vol.31 , pp. 81-118
    • Brassesco, S.1    De Masi, A.2    Presutti, E.3
  • 10
    • 0000063612 scopus 로고
    • Statistical mechanics of nonuniform magnetization reversal
    • Braun, H.B.: Statistical mechanics of nonuniform magnetization reversal. Phys. Rev. B 50, 16501-16521 (1994)
    • (1994) Phys. Rev. B , vol.50 , pp. 16501-16521
    • Braun, H.B.1
  • 11
    • 0029770296 scopus 로고    scopus 로고
    • The time cone method for nucleation and growth kinetics on a finite domain
    • Cahn, J.W.: The time cone method for nucleation and growth kinetics on a finite domain. Mat. Res. Soc. Symp. Proc. 398, 425-437 (1996)
    • (1996) Mat. Res. Soc. Symp. Proc , vol.398 , pp. 425-437
    • Cahn, J.W.1
  • 12
    • 0039845758 scopus 로고
    • Small random perturbations of infinite dimensional dynamical systems and nucleation theory
    • Cassandro, M., Olivieri, E., Picco, P.: Small random perturbations of infinite dimensional dynamical systems and nucleation theory. Ann. Inst. Henri Poincaré 44, 343-396 (1986)
    • (1986) Ann. Inst. Henri Poincaré , vol.44 , pp. 343-396
    • Cassandro, M.1    Olivieri, E.2    Picco, P.3
  • 13
    • 0031478723 scopus 로고    scopus 로고
    • Central limit theory for the number of seeds in a growth model in ℝd with inhomogeneous Poisson arrivals
    • Chiu, S.N., Quine, M.P.: Central limit theory for the number of seeds in a growth model in ℝd with inhomogeneous Poisson arrivals. Ann. Appl. Probab. 7, 802-814 (1997)
    • (1997) Ann. Appl. Probab , vol.7 , pp. 802-814
    • Chiu, S.N.1    Quine, M.P.2
  • 14
    • 2142825143 scopus 로고    scopus 로고
    • Second Order Partial Differential Equations in Hilbert Spaces
    • Cambridge University Press, Cambridge
    • Da Prato, G., Zabczyk, J.: Second Order Partial Differential Equations in Hilbert Spaces. London Mathematical Society Lecture Note Series, vol. 293. Cambridge University Press, Cambridge (2002)
    • (2002) London Mathematical Society Lecture Note Series , vol.293
    • Da Prato, G.1    Zabczyk, J.2
  • 16
    • 0040955183 scopus 로고    scopus 로고
    • Metropolis dynamics relaxation via nucleation and growth
    • Dehghanpour, P., Schonmann, R.H.: Metropolis dynamics relaxation via nucleation and growth. Commun. Math. Phys. 188, 89-119 (1997)
    • (1997) Commun. Math. Phys , vol.188 , pp. 89-119
    • Dehghanpour, P.1    Schonmann, R.H.2
  • 17
    • 4243825047 scopus 로고
    • Rigorous derivation of reaction-diffusion equations with fluctuations
    • De Masi, A., Ferrari, P.A., Lebowitz, J.L.: Rigorous derivation of reaction-diffusion equations with fluctuations. Phys. Rev. Lett. 55, 1947-1949 (1985)
    • (1985) Phys. Rev. Lett , vol.55 , pp. 1947-1949
    • De Masi, A.1    Ferrari, P.A.2    Lebowitz, J.L.3
  • 18
    • 0040365877 scopus 로고    scopus 로고
    • Glauber evolution with Kac potentials: III. Spinodal decomposition
    • De Masi, A., Orlandi, E., Presutti, E., Triolo, L.: Glauber evolution with Kac potentials: III. Spinodal decomposition. Nonlinearity 9, 53-114 (1996)
    • (1996) Nonlinearity , vol.9 , pp. 53-114
    • De Masi, A.1    Orlandi, E.2    Presutti, E.3    Triolo, L.4
  • 19
    • 0042340506 scopus 로고
    • Spatial patterns when phases separate in an interacting particle system
    • De Masi, A., Pellegrinotti, A., Presutti, E., Vares, M.E.: Spatial patterns when phases separate in an interacting particle system. Ann. Probab. 22, 334-371 (1994)
    • (1994) Ann. Probab , vol.22 , pp. 334-371
    • De Masi, A.1    Pellegrinotti, A.2    Presutti, E.3    Vares, M.E.4
  • 21
    • 33747589472 scopus 로고    scopus 로고
    • Towards a theory of transition paths
    • E, W
    • E, W., Vanden-Eijnden, E.: Towards a theory of transition paths. J. Stat. Phys. 123, 503-523 (2006)
    • (2006) J. Stat. Phys , vol.123 , pp. 503-523
    • Vanden-Eijnden, E.1
  • 22
    • 0000754401 scopus 로고
    • Large fluctuations for a nonlinear heat equation with noise
    • Faris, W.G., Jona-Lasinio, G.: Large fluctuations for a nonlinear heat equation with noise. J. Phys. A: Math. Gen. 15, 3025-3055 (1982)
    • (1982) J. Phys. A: Math. Gen , vol.15 , pp. 3025-3055
    • Faris, W.G.1    Jona-Lasinio, G.2
  • 24
    • 21844513537 scopus 로고
    • The scaling limit for a stochastic PDE and the separation of phases
    • Funaki, T.: The scaling limit for a stochastic PDE and the separation of phases. Probab. Theory Relat. Fields 102, 221-288 (1995)
    • (1995) Probab. Theory Relat. Fields , vol.102 , pp. 221-288
    • Funaki, T.1
  • 25
    • 38149147364 scopus 로고
    • Phase separation and random domain patterns in a stochastic particle model
    • Giacomin, G.: Phase separation and random domain patterns in a stochastic particle model. Stoch. Process. Appl. 51, 25-62 (1994)
    • (1994) Stoch. Process. Appl , vol.51 , pp. 25-62
    • Giacomin, G.1
  • 27
    • 0004320350 scopus 로고
    • Introduction to the Theory of Metastable and Unstable States
    • Springer, Berlin
    • Gunton, J.D., Droz, M.: Introduction to the Theory of Metastable and Unstable States. Lecture Notes in Physics, vol. 183. Springer, Berlin (1983)
    • (1983) Lecture Notes in Physics , vol.183
    • Gunton, J.D.1    Droz, M.2
  • 28
    • 35949034972 scopus 로고
    • Theory of dynamic critical phenomena
    • Halperin, P.C., Hohenberg, B.I.: Theory of dynamic critical phenomena. Rev. Mod. Phys. 49, 435-479 (1977)
    • (1977) Rev. Mod. Phys , vol.49 , pp. 435-479
    • Halperin, P.C.1    Hohenberg, B.I.2
  • 29
    • 0030502150 scopus 로고    scopus 로고
    • A general stochastic model for nucleation and growth
    • Holst, L., Quine, M.P., Robinson, J.: A general stochastic model for nucleation and growth. Ann. Appl. Probab. 6, 903-921 (1996)
    • (1996) Ann. Appl. Probab , vol.6 , pp. 903-921
    • Holst, L.1    Quine, M.P.2    Robinson, J.3
  • 30
    • 0000732349 scopus 로고
    • Reaction kinetics in processes of nucleation and growth
    • Johnson, W.A., Mehl, P.A.: Reaction kinetics in processes of nucleation and growth. Trans. Am. Inst. Min. Metall. Eng. 135, 416-442 (1939)
    • (1939) Trans. Am. Inst. Min. Metall. Eng , vol.135 , pp. 416-442
    • Johnson, W.A.1    Mehl, P.A.2
  • 31
    • 0000053713 scopus 로고
    • On the statistical theory of metal crystallization
    • Kolmogorov, A.N.: On the statistical theory of metal crystallization. Bull. Acad. Sci. USSR, Phys. Ser. 1, 355-360 (1937)
    • (1937) Bull. Acad. Sci. USSR, Phys. Ser , vol.1 , pp. 355-360
    • Kolmogorov, A.N.1
  • 32
    • 34547275473 scopus 로고
    • Brownian motion in a field of force and the diffusion theory of chemical reactions
    • Kramers, H.A.: Brownian motion in a field of force and the diffusion theory of chemical reactions. Physica 7, 284-304 (1940)
    • (1940) Physica , vol.7 , pp. 284-304
    • Kramers, H.A.1
  • 33
    • 36149007842 scopus 로고
    • Frequency factors in the thermally activated process
    • Landauer, R., Swanson, J.A.: Frequency factors in the thermally activated process. Phys. Rev. 121, 1668-1674 (1961)
    • (1961) Phys. Rev , vol.121 , pp. 1668-1674
    • Landauer, R.1    Swanson, J.A.2
  • 34
    • 29444451132 scopus 로고
    • Theory of the condensation point
    • Langer, J.S.: Theory of the condensation point. Ann. Phys. 41, 108-157 (1967)
    • (1967) Ann. Phys , vol.41 , pp. 108-157
    • Langer, J.S.1
  • 35
    • 0000782086 scopus 로고
    • Statistical theory of the decay of metastable states
    • Langer, J.S.: Statistical theory of the decay of metastable states. Ann. Phys. 54, 258-275 (1969)
    • (1969) Ann. Phys , vol.54 , pp. 258-275
    • Langer, J.S.1
  • 36
    • 0016568164 scopus 로고
    • Persistence of dynamical systems under random perturbations
    • Ludwig, D.: Persistence of dynamical systems under random perturbations. SIAM Rev. 17, 605-640 (1975)
    • (1975) SIAM Rev , vol.17 , pp. 605-640
    • Ludwig, D.1
  • 38
    • 0011521079 scopus 로고
    • Small random perturbations of finite- and infinite-dimensional dynamical systems: unpredictability of exit times
    • Martinelli, F., Olivieri, E., Scoppola, E.: Small random perturbations of finite- and infinite-dimensional dynamical systems: unpredictability of exit times. J. Stat. Phys. 55, 477-504 (1989)
    • (1989) J. Stat. Phys , vol.55 , pp. 477-504
    • Martinelli, F.1    Olivieri, E.2    Scoppola, E.3
  • 39
    • 0000506591 scopus 로고
    • The exit problem for randomly perturbed dynamical systems
    • Matkowsky, B.J., Schuss, Z.: The exit problem for randomly perturbed dynamical systems. SIAM J. Appl. Math. 33, 365-382 (1977)
    • (1977) SIAM J. Appl. Math , vol.33 , pp. 365-382
    • Matkowsky, B.J.1    Schuss, Z.2
  • 40
    • 0043069537 scopus 로고
    • Separation and domain structure of α+B 2 phase in Fe-Al alloys
    • Oki, K., Sagane, H., Eguchi, T.: Separation and domain structure of α+B 2 phase in Fe-Al alloys. J. Phys. C 7, 414 (1977)
    • (1977) J. Phys. C , vol.7 , pp. 414
    • Oki, K.1    Sagane, H.2    Eguchi, T.3
  • 41
    • 0036189628 scopus 로고    scopus 로고
    • Limit theorems for monotonic particle systems and sequential deposition
    • Penrose, M.D.: Limit theorems for monotonic particle systems and sequential deposition. Stoch. Process. Appl. 98, 175-197 (2002)
    • (2002) Stoch. Process. Appl , vol.98 , pp. 175-197
    • Penrose, M.D.1
  • 45
    • 13844309279 scopus 로고    scopus 로고
    • Invariant Measures of Stochastic partial differential equations and conditioned diffusions
    • Reznikoff, M.G., Vanden-Eijnden, E.: Invariant Measures of Stochastic partial differential equations and conditioned diffusions. C.R. Acad. Sci. Paris, Ser. I 340, 305-308 (2005)
    • (2005) C.R. Acad. Sci. Paris, Ser. I , vol.340 , pp. 305-308
    • Reznikoff, M.G.1    Vanden-Eijnden, E.2
  • 46
    • 0001444899 scopus 로고
    • Metastable lifetimes in a kinetic Ising model: Dependence on field and system size
    • Rikvold, P.A., Tomita, H., Miyashita, S., Sides, S.W.: Metastable lifetimes in a kinetic Ising model: Dependence on field and system size. Phys. Rev. E 49, 5080-5090 (1994)
    • (1994) Phys. Rev. E , vol.49 , pp. 5080-5090
    • Rikvold, P.A.1    Tomita, H.2    Miyashita, S.3    Sides, S.W.4
  • 47
    • 21344478931 scopus 로고
    • Slow droplet-driven relaxation of stochastic Ising models in the vicinity of the phase coexistence region
    • Schonmann, R.H.: Slow droplet-driven relaxation of stochastic Ising models in the vicinity of the phase coexistence region. Commun. Math. Phys. 161, 1-49 (1994)
    • (1994) Commun. Math. Phys , vol.161 , pp. 1-49
    • Schonmann, R.H.1
  • 48
    • 0032098595 scopus 로고    scopus 로고
    • Wulff droplets and the metastable relaxation of kinetic Ising models
    • Schonmann, R.H., Shlosman, S.B.: Wulff droplets and the metastable relaxation of kinetic Ising models. Commun. Math. Phys. 194, 389-462 (1998)
    • (1998) Commun. Math. Phys , vol.194 , pp. 389-462
    • Schonmann, R.H.1    Shlosman, S.B.2
  • 49
    • 0002044060 scopus 로고
    • Singular perturbation methods in stochastic differential equations of mathematical physics
    • Schuss, Z.: Singular perturbation methods in stochastic differential equations of mathematical physics. SIAM Rev. 22, 119-155 (1980)
    • (1980) SIAM Rev , vol.22 , pp. 119-155
    • Schuss, Z.1
  • 50
    • 0001227440 scopus 로고
    • Statistical properties of the relaxation processes of metastable states in the kinetic Ising model
    • Tomita, H., Miyashita, S.: Statistical properties of the relaxation processes of metastable states in the kinetic Ising model. Phys. Rev. B 46, 8886-8893 (1992)
    • (1992) Phys. Rev. B , vol.46 , pp. 8886-8893
    • Tomita, H.1    Miyashita, S.2


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