Brownian Motion -- from Eric Weisstein's World of Physics

The random walk $Eric Weisstein's World of Math$ motion of small particles suspended in a fluid due to bombardment by molecules obeying a Maxwellian velocity distribution. The phenomenon was first observed by Jan Ingenhousz

in 1785, but was subsequently rediscovered by Brown in 1828. Einstein

used kinetic theory to derive the diffusion constant for such motion in terms of fundamental parameters of the particles and liquid, and this equation was subsequently used by Perrin

to determine Avogadro's number. Brownian trajectories are continuous, but of infinite length between any two points.

Brown, R. "A Brief Account of Microscopical Observations Made in the Months on June, July, and August, 1827, on the Particles Contained in the Pollen of Plants; and on the General Existence of Active Molecules in Organic and Inorganic Bodies." Phil. Mag. 4, 161-173, 1828.

Chandrasekhar, S. "Stochastic Problems in Physics and Astronomy." Rev. Modern Phys. 15, 1-89, 1943. Reprinted in Noise and Stochastic Processes (Ed. N. Wax). New York: Dover, pp. 3-91, 1954.

Doob, J. L. "The Brownian Movement and Stochastic Equations." Ann. Math. 43, 351-369, 1942. Reprinted in Noise and Stochastic Processes (Ed. N. Wax). New York: Dover, pp. 319-337, 1954.

Einstein, A. "Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen." Ann. Phys. 17, 549, 1905.

Einstein, A. Investigations on the Theory of Brownian Movement. New York: Dover, 1956.

Finch, S. "Ornstein-Uhlenbeck Process." May 15, 2004. http://pauillac.inria.fr/algo/csolve/ou.pdf.

Kak, M. "Random Walk and the Theory of Brownian Motion." Amer. Math. Monthly 54, 369-391, 1947. Reprinted in Noise and Stochastic Processes (Ed. N. Wax). New York: Dover, pp. 295-317, 1954.

Reif, F. Fundamentals of Statistical and Thermal Physics. New York: McGraw-Hill, 1965.

Uhlenbeck, G. E. and Ornstein, L. S. "On the Theory of Brownian Motion." Phys. Rev. 36, 823-841, 1930. Reprinted in Noise and Stochastic Processes (Ed. N. Wax). New York: Dover, pp. 93-111, 1954.

Wang, M. C. and Uhlenbeck, G. E. "On the Theory of Brownian Motion II." Rev. Mod. Phys. 36, 323-342, 1945. Reprinted in Noise and Stochastic Processes (Ed. N. Wax). New York: Dover, pp. 113-132, 1954.

Weisstein, E. W. "Books about Brownian Motion." http://www.ericweisstein.com/encyclopedias/books/BrownianMotion.html.