Metastability under stochastic dynamics

Stochastic Processes and their Applications

Volumn 114, Issue 1, 2004, Pages 1-26

  den Hollander, F ^a  

^a EURANDOM   (Netherlands)

Author keywords

Critical droplet; Discrete isoperimetric inequalities; Interacting particle systems; Large deviations; Metastability; Potential theory; Stochastic dynamics

Indexed keywords

EID: 4644313263     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2004.07.007     Document Type: Article

References (58)

1. L. Alonso, R. Cerf, The three-dimensional polyominoes of minimal area, Electron. J. Combin. 3 (1996), research paper 27
2. G. Ben Arous, R. Cerf, Metastability of the three-dimensional Ising model on a torus at very low temperature, Electron. J. Probab. 1 (1996), research paper 10
3. N. Berglund B. Gentz The effect of additive noise on dynamical hysteresis Nonlinearity 15 2002 605-632
4. A. Bovier, Metastability and ageing in stochastic dynamics, in: A. Maass, S. Martinez, J. San Martin (Eds.), Dynamics and Randomness II, Santiago de Chile, 2002, Kluwer, Dordrecht 2004, pp. 17-81
5. A. Bovier M. Eckhoff V. Gayrard M. Klein Metastability in stochastic dynamics of disordered mean-field models Probab. Theory Related Fields 119 2001 99-161
6. A. Bovier M. Eckhoff V. Gayrard M. Klein Metastability and low lying spectra in reversible Markov chains Comm. Math. Phys. 228 2002 219-255
7. A. Bovier, M. Eckhoff, V. Gayrard, M. Klein, Metastability in reversible diffusion processes I. Sharp asymptotics for capacities and exit times, J. Eur. Math. Soc. 6 (2004)
8. A. Bovier, M. Eckhoff, V. Gayrard, M. Klein, Metastability in reversible diffusion processes II. Precise asymptotics for small eigenvalues, J. Eur. Math. Soc. 6 (2004)
9. A. Bovier, F. den Hollander, F.R. Nardi, Sharp asymptotics for Kawasaki dynamics on a finite box with open boundary, EURANDOM Report 2004-021, 2004; Probab. Theory Related Fields, in press
10. A. Bovier F. Manzo Metastability in Glauber dynamics in the low-temperature limit: Beyond exponential asymptotics J. Statist. Phys. 107 2002 757-779
11. D. Capocaccia M. Cassandro E. Olivieri A study of metastability in the Ising model Comm. Math. Phys. 39 1974 185-205
12. M. Cassandro A. Galves E. Olivieri M.E. Vares Metastable behavior of stochastic dynamics: A pathwise approach J. Statist. Phys. 35 1984 603-634
13. M. Cassandro E. Olivieri A rigorous study of metastability in a continuous model J. Statist. Phys. 17 1977 229-244
14. O. Catoni R. Cerf The exit path of a Markov chain with rare transitions ESAIM Probab. Statist. 1 1995 95-144
15. E.N.M. Cirillo A note on the metastability of the Ising model: The alternate updating case J. Statist. Phys. 106 2002 385-390
16. E.N.M. Cirillo F.R. Nardi Metastability for a stochastic dynamics with a parallel heat bath updating rule J. Statist. Phys. 110 2003 183-217
17. E.N.M. Cirillo E. Olivieri Metastability and nucleation for the Blume-Capel model: Different mechanisms of transition J. Statist. Phys. 83 1996 473-554
18. P. Dehghanpour R.H. Schonmann Metropolis dynamics relaxation via nucleation and growth Comm. Math. Phys. 188 1997 89-119
19. P. Dehghanpour R.H. Schonmann A nucleation-and-growth model Probab. Theory Related Fields 107 1997 123-135
20. P.G. Doyle, J.L. Snell, Random Walks and Electric Networks, Carus Mathematical Monographs 22, Mathematical Association of America, Washington DC, 1984
21. M.I. Freidlin A.D. Wentzell Random Perturbations of Dynamical Systems 1984 Springer Berlin
22. F. den Hollander F.R. Nardi E. Olivieri E. Scoppola Droplet growth for three-dimensional Kawasaki dynamics Probab. Theory Related Fields 125 2003 153-194
23. F. den Hollander, F.R. Nardi, E. Olivieri, E. Scoppola, Homogeneous nucleation for two-dimensional Kawasaki dynamics, in preparation
24. F. den Hollander E. Olivieri E. Scoppola Metastability and nucleation for conservative dynamics J. Math. Phys. 41 2000 1424-1498
25. F. den Hollander E. Olivieri E. Scoppola Nucleation in fluids: Some rigorous results Physica A 279 2000 110-122
26. F. den Hollander, E. Olivieri, E. Scoppola, Metastability and nucleation for conservative dynamics, in: Inhomogeneous Random Systems, Cergy-Pontoise, 2000, Markov Proc. Related Fields 7 (2001) 51-53
27. N.G. van Kampen Stochastic Processes in Physics and Chemistry 1981 North-Holland Amsterdam
28. R. Kotecký E. Olivieri Droplet dynamics for the asymmetric Ising model J. Statist. Phys. 70 1993 1121-1148
29. R. Kotecký E. Olivieri Shapes of growing droplets - a model of escape from a metastable phase J. Statist. Phys. 75 1994 409-506
30. J. Lebowitz O. Penrose Rigorous treatment of metastable states in van der Waals theory J. Statist. Phys. 3 1971 211-236
31. F. Manzo F.R. Nardi E. Olivieri E. Scoppola On the essential features of metastability: Tunneling time and critical configurations J. Statist. Phys. 115 2004 591-642
32. F. Manzo E. Olivieri Relaxation patterns for competing metastable states: a nucleation and growth model Markov Proc. Related Fields 4 1998 549-570
33. F. Manzo E. Olivieri Dynamical Blume-Capel model: competing metastable states at infinite volume J. Statist. Phys. 104 2001 1029-1090
34. F. Martinelli E. Olivieri E. Scoppola Metastability and exponential approach to equilibrium for low temperature stochastic Ising models J. Statist. Phys. 61 1990 1105-1119
35. F. Martinelli E. Olivieri E. Scoppola On the Swendsen-Wang dynamics. I. Exponential convergence to equilibrium J. Statist. Phys. 62 1991 117-133
36. F. Martinelli E. Olivieri E. Scoppola On the Swendsen-Wang dynamics. II. Critical droplets and homogeneous nucleation at low temperature for the two-dimensional Ising model J. Statist. Phys. 62 1991 135-159
37. P. Mathieu P. Picco Metastability and convergence to equilibrium for the random field Curie-Weiss model J. Statist. Phys. 91 1998 679-732
38. F. Nardi E. Olivieri Low temperature stochastic dynamics for an Ising model with alternating field Markov Proc. Related Fields 2 1996 117-166
39. E.J. Neves A discrete variational problem related to Ising droplets at low temperature J. Statist. Phys. 80 1995 103-123
40. E.J. Neves R.H. Schonmann Critical droplets and metastability for a Glauber dynamics at very low temperature Comm. Math. Phys. 137 1991 209-230
41. E.J. Neves R.H. Schonmann Behavior of droplets for a class of Glauber dynamics at very low temperature Probab. Theory Related Fields 91 1992 331-354
42. E. Olivieri E. Scoppola Markov chains with exponentially small transition probabilities: first exit problem from a general domain. I. The reversible case J. Statist. Phys. 79 1995 613-647
43. E. Olivieri E. Scoppola Markov chains with exponentially small transition probabilities: first exit problem from a general domain. II. The general case J. Statist. Phys. 84 1996 987-1041
44. E. Olivieri, E. Scoppola, Metastability and typical exit paths in stochastic dynamics, in: Proceedings of the European Congress of Mathematics, Budapest, 1996, vol. 2, Progress in Mathematics 169, Birkhäuser, Basel, 1998, pp. 124-150
45. E. Olivieri M.E. Vares Large Deviations and Metastability 2004 Cambridge University Press Cambridge
46. C. Peixoto Metastable behavior of low temperature Glauber dynamics with stirring J. Statist. Phys. 80 1995 1165-1184
47. O. Penrose J.L. Lebowitz Towards a rigorous molecular theory of metastability in: E.W. Montroll J.L. Lebowitz eds. Fluctuation Phenomena second ed. 1987 North-Holland Amsterdam
48. R.H. Schonmann, An approach to characterize metastability and critical droplets in stochastic Ising models, in: Multiscale Phenomena, São Paulo, 1990, Ann. Inst. H. Poincaré Phys. Théor. 55 (1991) 591-600
49. R.H. Schonmann The pattern of escape from metastability of a stochastic Ising model Comm. Math. Phys. 147 1992 231-240
50. R.H. Schonmann Relaxation times for stochastic Ising models in the limit of vanishing external field at fixed low temperatures in: N. Boccara E. Goles S. Martinez P. Picco eds. Cellular Automata and Cooperative Systems, Les Houches, 1992, NATO ASI Series 1993 Kluwer Academic Publishers Dordrecht 543-546
51. R.H. Schonmann Slow droplet-driven relaxation of stochastic Ising models in the vicinity of the phase coexistence region Comm. Math. Phys. 161 1994 1-49
52. R.H. Schonmann Theorems and conjectures on the droplet-driven relaxation of stochastic Ising models in: G. Grimmett ed. Probability and Phase Transition, Cambridge, 1993, NATO ASI Series 1994 Kluwer Academic Publishers Dordrecht 265-301
53. R.H. Schonmann, Metastability and the Ising model, in: Proceedings of the International Congress of Mathematics, Berlin, 1998, Doc. Math., Extra Vol. 3, pp. 173-181
54. R.H. Schonmann S. Shlosman Wulff droplets and the metastable relaxation of kinetic Ising models Comm. Math. Phys. 194 1998 389-462
55. E. Scoppola Renormalization group for Markov chains and application to metastability J. Statist. Phys. 73 1993 83-121
56. E. Scoppola Metastability for Markov chains A general procedure based on renormalization group ideas in: G. Grimmett ed. Probability and Phase Transition, Cambridge, 1993, NATO ASI Series 1994 Kluwer Academic Publishers Dordrecht 303-322
57. E. Scoppola Renormalization and graph methods for Markov chains in: Advances in Dynamical Systems and Quantum Physics, Capri, 1993 1995 World Scientific Publishing River Edge, NJ 260-281
58. M.E. Vares Large deviations and metastability in: Disordered Systems, Temuco, 1991/1992, Travaux en Cours 53 1996 Hermann Paris 1-62