Coarsening, nucleation, and the marked brownian web
Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) no. 1, pp. 37-60. 
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     title = {Coarsening, nucleation, and the marked brownian web},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {37--60},
     publisher = {Elsevier},
     volume = {42},
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Fontes, L. R. G.; Isopi, M.; Newman, C. M.; Ravishankar, K. Coarsening, nucleation, and the marked brownian web. Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) no. 1, pp. 37-60. doi : 10.1016/j.anihpb.2005.01.003. http://archive.numdam.org/articles/10.1016/j.anihpb.2005.01.003/

[1] R. Arratia, Coalescing Brownian motions and the voter model on Z, Unpublished partial manuscript (circa 1981), available from rarratia@math.usc.edu.

[2] L. Breiman, Probability, SIAM, 1992. | MR

[3] B. Derrida, V. Hakim, V. Pasquier, Exact exponent for the number of persistent spins in the zero-temperature dynamics of the one-dimensional Potts model, J. Statist. Phys. 85 (1996) 763-797. | MR | Zbl

[4] B. Derrida, R. Zeitak, Distribution of domain sizes in the zero temperature Glauber dynamics of the one-dimensional Potts model, Phys. Rev. E 54 (1996) 2513-2525.

[5] I. Fatkullin, E. Vanden-Eijnden, Coarsening by diffusion-annihilation in a bistable system driven by noise, Preprint, 2003. | MR

[6] I. Fatkullin, E. Vanden-Eijnden, Statistical description of contact-interacting Brownian particles on the line, J. Statist. Phys. 112 (2003) 155-163. | MR | Zbl

[7] L.R.G. Fontes, M. Isopi, C.M. Newman, K. Ravishankar, The Brownian web, Proc. Nat. Acad. Sci. 99 (2002) 15888-15893. | MR | Zbl

[8] L.R.G. Fontes, M. Isopi, C.M. Newman, K. Ravishankar, The Brownian web: characterization and convergence, Ann. Probab. 32 (2004) 2857-2883. | MR | Zbl

[9] L.R.G. Fontes, M. Isopi, C.M. Newman, K. Ravishankar, The Brownian web: characterization and convergence, Long version, math.PR/0304119.

[10] L.R.G. Fontes, M. Isopi, C.M. Newman, D.L. Stein, Aging in 1D discrete spin models and equivalent systems, Phys. Rev. Lett. 87 (2001) 110201.

[11] L.R.G. Fontes, M. Isopi, C.M. Newman, D.L. Stein, 1D aging, in preparation.

[12] H.-O. Georgii, Gibbs Measures and Phase Transitions, Walter de Gruyter, 1988. | MR | Zbl

[13] B. Granovsky, N. Madras, The noisy voter model, Stochastic Process. Appl. 55 (1995) 23-43. | MR | Zbl

[14] S. Habib, K. Lindenberg, G. Lythe, C. Molina-Paris, Diffusion-limited reaction in one dimension: paired and unpaired nucleation, J. Chem. Phys. 115 (2001) 73-89.

[15] S. Habib, G.D. Lythe, Dynamics of kinks: nucleation, diffusion and annihilation, Phys. Rev. Lett. 84 (2000) 1070-1073.

[16] T.E. Harris, Additive set-valued Markov processes and graphical methods, Ann. Probab. 6 (1978) 355-378. | MR | Zbl

[17] S. Karlin, H. Taylor, A First Course in Stochastic Processes, Academic Press, New York, 1975. | MR | Zbl

[18] P. Lévy, Processus Stochastiques et Mouvement Brownien, Gauthier-Villars, Paris, 1948. | MR | Zbl

[19] T.M. Liggett, Interacting Particle Systems, Springer-Verlag, New York, 1985. | MR | Zbl

[20] T.M. Liggett, Stochastic Interacting Systems: Contact, Voter and Exclusion Processes, Springer-Verlag, New York, 1999. | MR | Zbl

[21] 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. | MR | Zbl

[22] F. Soucaliuc, B. Tóth, W. Werner, Reflection and coalescence between independent one-dimensional Brownian paths, Ann. Inst. H. Poincaré Probab. Statist. 36 (2000) 509-545. | EuDML | Numdam | MR | Zbl

[23] S.J. Taylor, The α-dimensional measure of the graph and set of zeros of a Brownian path, Proc. Cambridge Philos. Soc. 51 (1955) 265-274. | Zbl

[24] B. Tóth, W. Werner, The true self-repelling motion, Probab. Theory Related Fields 111 (1998) 375-452. | MR | Zbl

[25] Y. Xiao, H. Lin, Dimension properties of sample paths of self-similar processes, Acta Math. Sinica (N.S.) 10 (1994) 289-300. | MR | Zbl

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