Center for diffusion of mathematic journals


Actes des rencontres du CIRM

Table of contents for this issue | Previous article | Next article
Bálint Tóth; Benedek Valkó
Superdiffusive bounds on self-repellent precesses in $d=2$ — extended abstract
Actes des rencontres du CIRM, 2 no. 1: Excess Self-Intersections & Related Topics (2010), p. 39-41, doi: 10.5802/acirm.23
Article PDF

Résumé - Abstract

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).


[1] D. Amit, G. Parisi, L. Peliti: Asymptotic behavior of the ‘true’ self-avoiding walk. Physical Reviews B 27: 1635–1645 (1983)  MR 690540
[2] R.T. Durrett, L.C.G.Rogers: Asymptotic behavior of Brownian polymers. Probability Theory and Related Fields 92: 337–349 (1992)  MR 1165516 |  Zbl 0767.60080
[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. (submitted, 2010) arXiv
[4] C. Landim, A. Ramirez, H-T. Yau: Superdiffusivity of two dimensional lattice gas models. Journal of Statistical Physics 119: 963–995 (2005)  MR 2157854 |  Zbl 1088.82016
[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)  MR 2034485 |  Zbl 1064.60164
[6] T. S. Mountford, P. Tarrès: An asymptotic result for Brownian polymers. Ann. Inst. H. Poincaré – Probab. Stat. 44: 29–46 (2008) Numdam |  MR 2451570 |  Zbl 1175.60084
[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+) arXiv
[9] B. Tóth: ‘True’ self-avoiding walk with bond repulsion on $\mathbb{Z}$: limit theorems. Ann. Probab., 23: 1523-1556 (1995) Article |  MR 1379158 |  Zbl 0852.60083
[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.  MR 1905343 |  Zbl 1101.82011
[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) arXiv
[12] B. Tóth, B. Vető: Continuous time ‘true’ self-avoiding random walk on $\mathbb{Z}$. ALEA – Latin Amrican Journal of Probability (2010, to appear) arXiv
[13] B. Tóth, W. Werner: The true self-repelling motion. Probab. Theory Rel. Fields, 111: 375-452 (1998)  MR 1640799 |  Zbl 0912.60056
[14] H-T. Yau: $(\log t)^{2/3}$ law of the two dimensional asymmetric simple exclusion process. Annals of Mathematics 159: 377–105 (2004)  MR 2052358 |  Zbl 1060.60099
Copyright Cellule MathDoc 2019 | Credit | Site Map