Brownian fluctuations of the interface in the D=1 Ginzburg-Landau equation with noise
S. Brassesco; A. De Masi; E. Presutti
Annales de l'I.H.P. Probabilités et statistiques (1995)
- Volume: 31, Issue: 1, page 81-118
- ISSN: 0246-0203
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topBrassesco, S., De Masi, A., and Presutti, E.. "Brownian fluctuations of the interface in the D=1 Ginzburg-Landau equation with noise." Annales de l'I.H.P. Probabilités et statistiques 31.1 (1995): 81-118. <http://eudml.org/doc/77510>.
@article{Brassesco1995,
author = {Brassesco, S., De Masi, A., Presutti, E.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Ginzburg-Landau equation; Neumann boundary conditions; instanton; Brownian motion},
language = {eng},
number = {1},
pages = {81-118},
publisher = {Gauthier-Villars},
title = {Brownian fluctuations of the interface in the D=1 Ginzburg-Landau equation with noise},
url = {http://eudml.org/doc/77510},
volume = {31},
year = {1995},
}
TY - JOUR
AU - Brassesco, S.
AU - De Masi, A.
AU - Presutti, E.
TI - Brownian fluctuations of the interface in the D=1 Ginzburg-Landau equation with noise
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1995
PB - Gauthier-Villars
VL - 31
IS - 1
SP - 81
EP - 118
LA - eng
KW - Ginzburg-Landau equation; Neumann boundary conditions; instanton; Brownian motion
UR - http://eudml.org/doc/77510
ER -
References
top- [1] R.J. Adler, An introduction to continuity, extrema, and related topics for general Gaussian processes, Lecture Notes-Monograph series, Institute of Mathematical Statistics, Vol. 42, 1990. Zbl0747.60039MR1088478
- [2] S. Allen and J. Cahn, A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening, Acta Metall., Vol. 27, 1979, pp. 1084-1095.
- [3] S. Brassesco, Stability of the instanton under small random perturbations, to appear in Stoch. Proc. App., 1994. Zbl0815.60051MR1307343
- [4] J. Carr and B. Pego, Metastable patterns in solutions of ut = ∈2uxx + u(1 - u2), Commun. Pure Applied Math., Vol. 42, 1989, pp. 523-576. Zbl0685.35054MR997567
- [5] M. Cassandro, E. Orlandi and E. Presutti, Interfaces and typical Gibbs configurations for one dimensional Kac potentials, Prob. Theory Rel. Fields, Vol. 96, 1993, pp. 57-96. Zbl0791.60096MR1222365
- [6] A. De Masi and E. Presutti, Mathematical methods for hydrodynamical limits, Lecture Notes in Mathematics, Springer-Verlag, Berlin, Heidelberg, New York, Vol. 1501, 1991. Zbl0754.60122MR1175626
- [7] G.F. Dell'Antonio, Methods of stochastic stability of the Gribov horizon in the stochastic quantization of gauge theories, Lecture Notes in Physics, Proceedings of the 1988 Ascona Conference, Springer Verlag, 1988.
- [8] G. Da Prato and J. Zabczyk, Stochastic equations in infinite dimensions, Encyclopedia of Mathematics and its Applications, Cambridge University Press, 1992. Zbl0761.60052MR1207136
- [9] A. De Masi, T. Gobron and E. Presutti, Travelling fronts in non local evolution equations, Preprint, 1993. Zbl0847.45008
- [10] C.R. Doering, Nonlinear parabolic stochastic differential equations with additive colored noise on R x R+: a regulated stochastic quantization, Comm. Math. Phys., Vol. 109, 1987, pp. 537-561. Zbl0625.60069MR885561
- [11] W. Paris and G. Jona-Lasinio, Large fluctuations for a nonlinear heat equation with noise, J. Phys., Vol. A 15, 1982, pp. 3025-3055. Zbl0496.60060MR684578
- [12] P. Fife and J.B. Mcleod, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Arch. Rat. Mech. Anal., Vol. 65, 1977, pp. 335-361. Zbl0361.35035MR442480
- [13] T. Funaki, The scaling limit for a stochastic PDE and the separation of phases, preprint, 1993. MR1337253
- [14] G. Fusco, A geometric approach to the dynamics of ut = ∈2 uxx + f(u) for small ∈, Lecture Notes in Physics, Springer-Verlag, Vol. 359, 1990, pp. 53-73. Zbl0715.35038MR1062209
- [15] G. Fusco and J. Hale, Slow-motion manifolds, dormant instability and singular perturbations, J. Dynamics Differential equations, Vol. 1, 1989, pp. 75-94. Zbl0684.34055MR1010961
- [16] P.C. Hohenberg and P.I. Halperin, Theory of dynamicl critical phenomena, Rev. Mod. Phys., Vol. 49, 1977, pp. 453-479.
- [17] D. Revuz and M. Yor, Continuous martingales and brownian motion, Springer Verlag, Heidelberg, Berlin, New York, 1991. Zbl0731.60002MR1083357
- [18] J.B. Walsh, A stochastic model of Neural Response, Adv. Appl. Prob., Vol. 13, 1981, pp. 231-281. Zbl0471.60083MR612203
- [19] J.B. Walsh, An introduction to stochastic partial differential equations, Lecture Notes in Mathematics, Vol. 1180, Springer-Verlag, 1984, pp. 265-437. Zbl0608.60060MR876085
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