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  • Tome 2 (2010)
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  • p. 39-41
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no. 1

Superdiffusive bounds on self-repellent precesses in d=2 — extended abstract
Bálint Tóth ; Benedek Valkó
Actes des rencontres du CIRM, Tome 2 (2010) no. 1, pp. 39-41.
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We prove superdiffusivity with multiplicative logarithmic corrections for a class of models of random walks and diffusions with long memory. The family of models includes the “true” (or “myopic”) self-avoiding random walk, self-repelling Durrett-Rogers polymer model and diffusion in the curl-field of (mollified) massless free Gaussian field in 2D. We adapt methods developed in the context of bulk diffusion of ASEP by Landim-Quastel-Salmhofer-Yau (2004).

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Publié le : 2011-01-03
DOI : https://doi.org/10.5802/acirm.23
@article{ACIRM_2010__2_1_39_0,
     author = {B\'alint T\'oth and Benedek Valk\'o},
     title = {Superdiffusive bounds on self-repellent precesses in $d=2$ --- extended abstract},
     journal = {Actes des rencontres du CIRM},
     pages = {39--41},
     publisher = {CIRM},
     volume = {2},
     number = {1},
     year = {2010},
     doi = {10.5802/acirm.23},
     language = {en},
     url = {https://acirm.centre-mersenne.org/articles/10.5802/acirm.23/}
}
Tóth, Bálint; Valkó, Benedek. Superdiffusive bounds on self-repellent precesses in $d=2$ — extended abstract. Actes des rencontres du CIRM, Tome 2 (2010) no. 1, pp. 39-41. doi : 10.5802/acirm.23. https://acirm.centre-mersenne.org/articles/10.5802/acirm.23/
  • Bibliographie

[1] D. Amit, G. Parisi, L. Peliti: Asymptotic behavior of the ‘true’ self-avoiding walk. Physical Reviews B 27: 1635–1645 (1983)

[2] R.T. Durrett, L.C.G.Rogers: Asymptotic behavior of Brownian polymers. Probability Theory and Related Fields 92: 337–349 (1992)

[3] I. Horváth, B. Tóth, B. Vető: Diffusive limits for “true” (or myopic) self-avoiding random walks and self-repellent Brownian polymers in three and more dimensions. http://arxiv.org/abs/1009.0401 (submitted, 2010)

[4] C. Landim, A. Ramirez, H-T. Yau: Superdiffusivity of two dimensional lattice gas models. Journal of Statistical Physics 119: 963–995 (2005)

[5] C. Landim, J. Quastel, M. Salmhofer, H-T. Yau: Superdiffusivity of one and two dimentsional asymmetric simple exclusion processes. Communicarions in Mathematical Physics 244: 455–481 (2004)

[6] T. S. Mountford, P. Tarrès: An asymptotic result for Brownian polymers. Ann. Inst. H. Poincaré – Probab. Stat. 44: 29–46 (2008)

[7] J. Quastel, B. Valkó: in preparation (2010)

[8] P. Tarrès, B. Tóth, B. Valkó: Diffusivity bounds for 1d Brownian polymers. Annals of Probability (to appear 2010+) http://arxiv.org/abs/0911.2356

[9] B. Tóth: ‘True’ self-avoiding walk with bond repulsion on ℤ: limit theorems. Ann. Probab., 23: 1523-1556 (1995)

[10] B. Tóth: Self-interacting random motions. In: Proceedings of the 3rd European Congress of Mathematics, Barcelona 2000, vol. 1, pp. 555-565, Birkhauser, 2001.

[11] P. Tarrès, B. Tóth, B. Valkó: Superdiffusive bounds on self-repellent Brownian polymers and diffusion in the curl of the free Gaussian field in d=2. (2010, in preparation)

[12] B. Tóth, B. Vető: Continuous time ‘true’ self-avoiding random walk on ℤ. ALEA – Latin Amrican Journal of Probability (2010, to appear) http://arxiv.org/abs/0909.3863

[13] B. Tóth, W. Werner: The true self-repelling motion. Probab. Theory Rel. Fields, 111: 375-452 (1998)

[14] H-T. Yau: (logt) 2/3 law of the two dimensional asymmetric simple exclusion process. Annals of Mathematics 159: 377–105 (2004)

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