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References

  • Bertini, Lorenzo; Brassesco, Stella; Buttà, Paolo. Soft and hard wall in a stochastic reaction diffusion equation. Arch. Ration. Mech. Anal. 190 (2008), no. 2, 307--345. MR2448321
  • Bertini, Lorenzo; Brassesco, Stella; Buttà, Paolo. Dobrushin states in the $\phi^ 4_ 1$ model. Arch. Ration. Mech. Anal. 190 (2008), no. 3, 477--516. MR2448325
  • Betz, Volker; Lőrinczi, József. Uniqueness of Gibbs measures relative to Brownian motion. Ann. Inst. H. Poincaré Probab. Statist. 39 (2003), no. 5, 877--889. MR1997216
  • Bogachev, Vladimir I. Gaussian measures. Mathematical Surveys and Monographs, 62. American Mathematical Society, Providence, RI, 1998. xii+433 pp. ISBN: 0-8218-1054-5 MR1642391
  • Brassesco, S.; De Masi, A.; Presutti, E. Brownian fluctuations of the interface in the $D=1$ Ginzburg-Landau equation with noise. Ann. Inst. H. Poincaré Probab. Statist. 31 (1995), no. 1, 81--118. MR1340032
  • Cassandro, Marzio; Orlandi, Enza; Presutti, Errico. Interfaces and typical Gibbs configurations for one-dimensional Kac potentials. Probab. Theory Related Fields 96 (1993), no. 1, 57--96. MR1222365
  • den Hollander, Frank. Large deviations. Fields Institute Monographs, 14. American Mathematical Society, Providence, RI, 2000. x+143 pp. ISBN: 0-8218-1989-5 MR1739680
  • Faris, William G.; Jona-Lasinio, Giovanni. Large fluctuations for a nonlinear heat equation with noise. J. Phys. A 15 (1982), no. 10, 3025--3055. MR0684578
  • Feynman, R. P. Space-time approach to non-relativistic quantum mechanics. Rev. Modern Physics 20, (1948). 367--387. MR0026940
  • Freidlin, Mark I. Random perturbations of reaction-diffusion equations: the quasideterministic approximation. Trans. Amer. Math. Soc. 305 (1988), no. 2, 665--697. MR0924775
  • Freidlin, M. I.; Wentzell, A. D. Random perturbations of dynamical systems. Translated from the 1979 Russian original by Joseph Szücs. Second edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 260. Springer-Verlag, New York, 1998. xii+430 pp. ISBN: 0-387-98362-7 MR1652127
  • Funaki, T. The scaling limit for a stochastic PDE and the separation of phases. Probab. Theory Related Fields 102 (1995), no. 2, 221--288. MR1337253
  • M. Hairer. An Introduction to Stochastic PDEs. phArXiv e-prints .
  • Jona-Lasinio, G.; Martinelli, F.; Scoppola, E. New approach to the semiclassical limit of quantum mechanics. I. Multiple tunnelings in one dimension. Comm. Math. Phys. 80 (1981), no. 2, 223--254. MR0623159
  • Kifer, Ju. I. Some results concerning small random perturbations of dynamical systems. (Russian) Teor. Verojatnost. i Primenen. 19 (1974), 514--532. MR0353451
  • Modica, Luciano; Mortola, Stefano. Un esempio di $\Gamma ^{-}$-convergenza. (Italian) Boll. Un. Mat. Ital. B (5) 14 (1977), no. 1, 285--299. MR0445362
  • R. Peierls. On Ising's model of ferromagnetism. phMathematical Proceedings of the Cambridge Philosophical Society, 32, (1936), 477--481.
  • Revuz, Daniel; Yor, Marc. Continuous martingales and Brownian motion. Third edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 293. Springer-Verlag, Berlin, 1999. xiv+602 pp. ISBN: 3-540-64325-7 MR1725357
  • Reznikoff, Maria G.; Vanden-Eijnden, Eric. Invariant measures of stochastic partial differential equations and conditioned diffusions. C. R. Math. Acad. Sci. Paris 340 (2005), no. 4, 305--308. MR2121896
  • Simon, Barry. Functional integration and quantum physics. Pure and Applied Mathematics, 86. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1979. ix+296 pp. ISBN: 0-12-644250-9 MR0544188
  • Vanden-Eijnden, Eric; Westdickenberg, Maria G. Rare events in stochastic partial differential equations on large spatial domains. J. Stat. Phys. 131 (2008), no. 6, 1023--1038. MR2407378
  • Varadhan, S. R. S. Large deviations and applications. CBMS-NSF Regional Conference Series in Applied Mathematics, 46. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1984. v+75 pp. ISBN: 0-89871-189-4 MR0758258
  • Weber, Hendrik. Sharp interface limit for invariant measures of a stochastic Allen-Cahn equation. Comm. Pure Appl. Math. 63 (2010), no. 8, 1071--1109. MR2642385
  • A. D. Wentzell and M. I. Freidlin. O malykh sluchainykh vozmuschcheniyakh dinamicheskikh sistem. phUspekhi Mat. Nauk 25, no. 1, (1970), 3-55. English translation of title: On small random perturbations of dynamical systems.
  • Zabczyk, J. Symmetric solutions of semilinear stochastic equations. Stochastic partial differential equations and applications, II (Trento, 1988), 237--256, Lecture Notes in Math., 1390, Springer, Berlin, 1989. MR1019609
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