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A random process consisting of a sequence of discrete steps of fixed length. The random thermal perturbations in a liquid
are responsible for a random walk phenomenon known as Brownian motion, 
and the
collisions of molecules in a gas are a random walk responsible for diffusion. Random walks
have interesting mathematical properties that vary greatly depending on the dimension in which the walk occurs and whether
it is confined to a lattice.
See also Random Walk--1-D, Random Walk--2-D, Random Walk--3-D, Self-Avoiding Walk
References
Barber, M. N. and Ninham, B. W. Random and Restricted Walks: Theory and Applications.
New York: Gordon and Breach, 1970.
Chandrasekhar, S. In Selected Papers on Noise and Stochastic Processes (Ed. N. Wax). New York: Dover, 1954.
Doyle, P. G. and Snell, J. L. Random Walks and Electric Networks. Washington, DC: Math. Assoc. Amer, 1984.
Dykin, E. B. and Uspenskii, V. A. Random Walks. New York: Heath, 1963.
Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd ed. New York: Wiley, 1968.
Gardner, M. ``Random Walks.'' Ch. 6-7 in
Mathematical Circus: More Puzzles, Games, Paradoxes, and Other Mathematical Entertainments.
Washington, DC: Math. Assoc. Amer., 1992.
Hughes, B. D. Random Walks and Random Environments, Vol. 1: Random Walks. New York: Oxford University Press, 1995.
Hughes, B. D. Random Walks and Random Environments, Vol. 2: Random Environments. New York: Oxford University Press, 1996.
Lawler, G. F. Intersections of Random Walks. Boston, MA: Birkhäuser, 1996.
Spitzer, F. Principles of Random Walk, 2nd ed. New York: Springer-Verlag, 1976.
Random Walks