Microscopic approach to random walks

Journal of Statistical Physics

Volumn 133, Issue 1, 2008, Pages 159-167

  Zaburdaev, Vasily Yu ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Aging; Continuous time random walk model; Coupled random walks; Two point probability function

Indexed keywords

EID: 52149089882     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-008-9598-8     Document Type: Article

References (34)

1. E.W. Montroll G.H. Weiss 1965 Random walk on lattices. II J. Math. Phys. 6 167 181
2. Montroll, E.W., Shlesinger, M.F.: Nonequilibrium Phenomena II: From Stochastic to Hydrodynamics. In: Leibowitz, J., Montroll, E.W. (eds.) Studies in Statistical Mechanics, vol. 11, pp. 1-122. North-Holland, Amsterdam (1984)
3. J.P. Bouchaud A. Georges 1990 Anomalous diffusion in disordered media-statistical mechanisms, models and physical applications Phys. Rep. 195 4-5 127 293
4. R. Metzler J. Klafter 2000 The random walk's guide to anomalous diffusion: a fractional dynamics approach Phys. Rep. 339 1 1 77
5. V.V. Uchaikin 2003 Self-similar anomalous diffusion and Levy-stable laws Phys. Uspekhi 46 821 849
6. Podlubny, I.: Fractional Differential Equations, p. 1. Academic Press, San Diego (1999)
7. Hilfer, R. (ed.): Applications of Fractional Calculus in Physics, p. 1. World Scientific, Singapore (2000)
8. R. Metzler J. Klafter 2004 The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics J. Phys. A 37 R161 R208
9. D. Brockmann L. Hufnagel T. Geisel 2006 The scaling laws of human travel Nature 439 7075 462 465
10. L. Hufnagel D. Brockmann T. Geisel 2004 Forecast and control of epidemics in a globalized world Proc. Natl. Acad. Sci. 101 42 15124 15129
11. Klafter, J., Sokolov, I.M.: Anomalous diffusion spreads its wings. Phys. World 18(8) (2005)
12. G. Ramos-Fernández J.L. Mateos O. Miramontes 2004 Levy walk patterns in the foraging movements of spider monkeys (Ateles geoffroyi) Behav. Ecol. Sociobiol. 55 223 230
13. Struick, L.C.E.: Physical Aging in Amorphous Polymers and Other Materials. Elsevier, Amsterdam (1978)
14. Bouchaud, J.P., Cugliandolo, L.F., Mézard, M., Kurchan, J.: In: Young, A.P. (ed.) Spin Glasses and Random Fields. World Scientific, Singapore (1997)
15. V. Dupuis V E. Vincent J.P. Bouchaud J. Hammann A. Ito H.A. Katori 2001 Aging, rejuvenation, and memory effects in Ising and Heisenberg spin glasses Phys. Rev. B 64 174204
16. M. Bellour A. Knaebel J.L. Harden F. Lequeux J.P. Munch 2003 Aging processes and scale dependence in soft glassy colloidal suspensions Phys. Rev. E 67 031405
17. C. Josserand A.V. Tkachenko D.M. Mueth H.M. Jaeger 2000 Memory effects in granular materials Phys. Rev. Lett. 85 3632
18. P. Le Doussal C. Monthus D.S. Fisher 1999 Random walkers in one-dimensional random environments: Exact renormalization group analysis Phys. Rev. E 59 4795
19. G. Aquino M. Bologna P. Grigolini B.J. West 2004 Aging and rejuvenation with fractional derivatives Phys. Rev. E 70 036105
20. P. Allegrini G. Aquino P. Grigolini L. Palatella A. Rosa 2003 Generalized master equation via aging continuous-time random walks Phys. Rev. E 68 056123
21. E. Barkai 2003 Aging in subdiffusion generated by a deterministic dynamical system Phys. Rev. Lett. 90 104101
22. E. Barkai Y.C. Cheng 2003 Aging continuous time random walks J. Chem. Phys. 118 6167
23. I.M. Sokolov A. Blumen J. Klafter 2001 Dynamics of annealed systems under external fields: CTRW and the fractional Fokker-Planck equations Europhys. Lett. 56 175
24. A. Baule R. Friedrich 2007 A fractional diffusion equation for two-point probability distributions of a continuous-time random walk Europhys. Lett. 77 10002
25. Barkai, E., Sokolov, I.M.: Multi-point distribution function for the continuous time random walk. J. Stat. Mech. P08001 (2007)
26. K.V. Chukbar 1995 Stochastic transfer and fractional derivatives J. Exp. Theor. Phys. 81 1025 1029
27. V.Yu. Zaburdaev K.V. Chukbar 2002 Enhanced superdiffusion and finite velocity of Levy flights J. Exp. Theor. Phys. 94 252 259
28. V.Yu. Zaburdaev K.V. Chukbar 2003 Memory effects in stochastic transport JETP Lett. 77 551 555
29. Zaburdaev, V.Yu., Sokolov, I.M.: Fractional diffusion equation for aging and equilibrated random walks. Phys. Rev. E (2008, submitted)
30. V.Yu. Zaburdaev 2006 Random walk model with waiting times depending on the preceding jump length J. Stat. Phys. 123 4 871 880
31. M.F. Shlesinger J. Klafter Y.M. Wong 1982 Random walks with infinite spatial and temporal moments J. Stat. Phys. 27 499 512
32. J. Klafter A. Blumen M.F. Shlesinger 1987 A stochastic pathway to anomalous diffusion Phys. Rev. A 35 3081 3085
33. T. Geisel J. Nierwetberg A. Zacherl 1985 Accelerated diffusion in Josephson junctions and related chaotic systems Phys. Rev. Lett. 54 616 619
34. M.F. Shlesinger J. Klafter 1989 Random walks in liquids J. Phys. Chem. 93 7023 7026