Dynamical windings of random walks and exclusion models. Part I: Thermodynamic limit in ℤ2

Journal of Statistical Physics

Volumn 114, Issue 1-2, 2004, Pages 229-260

  Fayolle, Guy ^a   Furtlehner, Cyril ^a  

^a INRIA   (France)

Author keywords

Burgers equation; Exclusion process; Phase transition; Random walks; Winding

Indexed keywords

EID: 3542990912     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/b:joss.0000003111.88829.9d     Document Type: Article

References (22)

1. C. L. Berthelsen, J. Glazier, and M. Skolnick, Global fractal dimension of human DNA sequences treated as pseudorandom walks, Phys. Rev. A 45:8902-8913 (1992).
2. O. Bénichoux and J. Desbois, Windings of the 2d free rouse chain, J. Phys. A. Math. Gen. 33:6655-6667 (2000).
3. J. Burgers, A mathematical model illustrating the theory of turbulences, Adv. Opal. Mech. 1:171-199 (1948).
4. S. Cebrat and M. Dudek, The effect of DNA phase structure on DNA walks, Eur. J. Phys. 3:271-276 (1998).
5. M. Clincy, B. Derrida, and M. Evans, Phase Transition in the ABC Model, cond/mat 0209674 (2002).
6. A. Comtet, J. Desbois, and S. Ouvry, Winding of planar brownian curves, J. Phys. A: Math. Gen. 23:3563-3572 (1990).
7. B. Derrida, M. Evans, V. Hakim, and V. Pasquier, Exact solution for 1d asymmetric exclusion model using a matrix formulation, J. Phys. A: Math. Gen. 26:1493-1517 (1993).
8. M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Oxford University Press, 1986).
9. R. Durrett, Ten lectures on particle system, in Lecture Notes in Maths., Vol. 1608 (Springer, 1995), pp. 97-201.
10. M. Evans, D. P. Foster, C. Godrèche, and D. Mukamel, Spontaneous symmetry breaking in a one dimensional driven diffusive system, Phys. Rev. Lett. 74:208-211 (1995).
11. P. D. Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, NY, 1979).
12. O. Kallenberg, Foundations of Modern Probability, 2nd Ed. (Springer, 2001).
13. M. Kardar, G. Parisi, and Y. Zhang, Dynamic scaling of growing interfaces, Phys. Rev. Lett. 56:889-892 (1986).
14. J. Komlos, G. Major, and P. Tusnady, An approximation of partial sums of independent rv's and the sample df i,ii., Z. Warsch. verw. Gebiete 32:111-131 (1975, 1976).
15. B. Øksendal, Stochastic Differential Equations (Springer, 1985).
16. R. Lahiri, M. Barma, and S. Ramaswamy, Strong phase separation in a model of sedimenting lattices, Phys. Rev. E 61:1648-1658 (2000).
17. T. M. Liggett, Interacting Particle Systems, Grundlehren der mathematischen Wissenschaften (Springer, 1985).
18. P. Lévy, Processus stochastiques et mouvement Brownien (Gauthier-Villars, 1948).
19. J. W. Pitman and M. Yor, Further asymptotic laws of planar brownian motion, Ann. Probab. 17:965-1011 (1989).
20. P. Rouse, A theory of linear viscoelastic properties of dilute solutions of coiling polymers, J. Chem. Phys. 21:1272-1280 (1953).
21. F. Spitzer, Some theorems concerning 2-dimensional brownian motion, Trans. Amer. Math. Soc. 87:187-197 (1958).
22. H. Spohn, Large Scale Dynamics of Interacting Particles (Springer, 1991).