Abstract
These are introductory lectures on random walks given by B. Derrida at the School on Disorder and Mixing (Cargèse, June 1987). The writing of these lectures was done in close collaboration with J.P. Bouchaud and A. Georges. These lectures present some basic results and questions about random walks in pure media, such as: the central limit theorem, diffusion law, number of different sites visited, number of self intersections; self avoiding walks, true self avoiding walks, Flory approximation, etc. They also give an introduction to random walks in random media (equivalence with the masses and springs network, density of states and autocorrelation function, spectral dimension, Einstein’s relation in disordered media). A simple discussion of the mechanisms leading to anomalous diffusion laws in heterogeneous media is given in part B.
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References
J.W. Haus, K.W. Kehr, Phys. Rep. 150, 265 (1987).
S. Havlin, D. Ben Avram, to appear in Adv. in Phys. (1987).
E.W. Montroll, B.J. West in Fluctuations phenomena, ed. Montroll-Lebowitz, North-Holland (1979).
D. Amit, G. Parisi, L. Peliti, Phys. Rev. 27, 1635 (1983); see also ref. A.12.
P.G. de Gennes, Scaling concepts in Polymer Physics (Cornell University Press, 1985).
D.S. McKenzie, Phys. Rep. C27, 35 (1976).
D. Klein, J. Stat Phys. 23, 561 (1980).
See e.g. H.E. Stanley, RJ. Reynolds, S. Redner, F. Family, in Real Space Renormalisation, T.W. Burkhardt, J.W. Van Leuwen Eds, Springer (1982).
N. Madras, A. Sokal, J. Stat. Phys. 47, 573 (1987).
W. Feller, An introduction to probability theory and its application. New York Wiley (1971).
Theoretical: J.C. Le Guillou, J. Zinn Justin, Phys. Rev. B2, 3976 (1980);
Experimental: J.P. Cotton, J. Physique (Lettres) 41, L23 (1980).
L. Peliti and L. Pietronero, Random Walks with Memory, Rivista del Nuovo Cimento 6, 1 (1987).
R. Rammal, J.C. Angles d’Auriac, A. Benoit, J. Phys. Lett. 17, L9 (1984).
S. Alexander, J. Bernasconi, W. Schneider, R. Orbach, Rev. Mod. Phys. 53, 175 (1981).
R. Rammal, G. Toulouse, J. Physique 44, L13 (1983).
R. Friedberg, O. Martin, J. Physique 47, 1663 (1986).
S. Alexander, R. Orbach, J. Phys. Lett. 43, L625 (1982).
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© 1988 Kluwer Academic Publishers
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Derrida, B., Bouchaud, J.P., Georges, A. (1988). Introduction to Random Walks. In: Guyon, E., Nadal, JP., Pomeau, Y. (eds) Disorder and Mixing. NATO ASI Series, vol 152. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2825-1_1
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DOI: https://doi.org/10.1007/978-94-009-2825-1_1
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