Coarsening, nucleation, and the marked brownian web

 Access to full text

 Full (PDF)

1. [1] R. Arratia, Coalescing Brownian motions and the voter model on $Z$, Unpublished partial manuscript (circa 1981), available from rarratia@math.usc.edu. 
2. [2] L. Breiman, Probability, SIAM, 1992. MR1163370
3. [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. Zbl0937.82005MR1418811
4. [4] B. Derrida, R. Zeitak, Distribution of domain sizes in the zero temperature Glauber dynamics of the one-dimensional Potts model, Phys. Rev. E54 (1996) 2513-2525. 
5. [5] I. Fatkullin, E. Vanden-Eijnden, Coarsening by diffusion-annihilation in a bistable system driven by noise, Preprint, 2003. MR1991034
6. [6] I. Fatkullin, E. Vanden-Eijnden, Statistical description of contact-interacting Brownian particles on the line, J. Statist. Phys.112 (2003) 155-163. Zbl1024.60043MR1991034
7. [7] L.R.G. Fontes, M. Isopi, C.M. Newman, K. Ravishankar, The Brownian web, Proc. Nat. Acad. Sci.99 (2002) 15888-15893. Zbl1069.60068MR1944976
8. [8] L.R.G. Fontes, M. Isopi, C.M. Newman, K. Ravishankar, The Brownian web: characterization and convergence, Ann. Probab.32 (2004) 2857-2883. Zbl1105.60075MR2094432
9. [9] L.R.G. Fontes, M. Isopi, C.M. Newman, K. Ravishankar, The Brownian web: characterization and convergence, Long version, math.PR/0304119. Zbl1105.60075
10. [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. [11] L.R.G. Fontes, M. Isopi, C.M. Newman, D.L. Stein, 1D aging, in preparation. 
12. [12] H.-O. Georgii, Gibbs Measures and Phase Transitions, Walter de Gruyter, 1988. Zbl0657.60122MR956646
13. [13] B. Granovsky, N. Madras, The noisy voter model, Stochastic Process. Appl.55 (1995) 23-43. Zbl0813.60096MR1312146
14. [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. [15] S. Habib, G.D. Lythe, Dynamics of kinks: nucleation, diffusion and annihilation, Phys. Rev. Lett.84 (2000) 1070-1073. 
16. [16] T.E. Harris, Additive set-valued Markov processes and graphical methods, Ann. Probab.6 (1978) 355-378. Zbl0378.60106MR488377
17. [17] S. Karlin, H. Taylor, A First Course in Stochastic Processes, Academic Press, New York, 1975. Zbl0315.60016MR356197
18. [18] P. Lévy, Processus Stochastiques et Mouvement Brownien, Gauthier-Villars, Paris, 1948. Zbl0034.22603MR190953
19. [19] T.M. Liggett, Interacting Particle Systems, Springer-Verlag, New York, 1985. Zbl0559.60078MR776231
20. [20] T.M. Liggett, Stochastic Interacting Systems: Contact, Voter and Exclusion Processes, Springer-Verlag, New York, 1999. Zbl0949.60006MR1717346
21. [21] E.J. Neves, R.H. Schonmann, Behavior of droplets for a class of Glauber dynamics at very low temperature, Probab. Theory Related Fields91 (1992) 331-354. Zbl0739.60101MR1151800
22. [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. Zbl0968.60072MR1785393
23. [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. Zbl0064.05201
24. [24] B. Tóth, W. Werner, The true self-repelling motion, Probab. Theory Related Fields111 (1998) 375-452. Zbl0912.60056MR1640799
25. [25] Y. Xiao, H. Lin, Dimension properties of sample paths of self-similar processes, Acta Math. Sinica (N.S.)10 (1994) 289-300. Zbl0813.60042MR1415699

1. Cristian Coletti, Glauco Valle, Convergence to the brownian Web for a generalization of the drainage network model
2. C. M. Newman, K. Ravishankar, E. Schertzer, Marking (1, 2) points of the brownian web and applications