Levy flight

A Lévy flight, named for French mathematician Paul Lévy, is a random walk in which the step-lengths have a probability distribution that is heavy-tailed. When defined as a walk in a space of dimension greater than one, the steps made are in isotropic random directions.

The term “Lévy flight” was coined by Benoît Mandelbrot, who used this for one specific definition of the distribution of step sizes. He used the term Cauchy flight for the case where the distribution of step sizes is a Cauchy distribution, and Rayleigh flight for when the distribution is a normal distribution.

Later researchers have extended the use of the term “Lévy flight” to include cases where the random walk takes place on a discrete grid rather than on a continuous space.

A Lévy flight is a random walk in which the steps are defined in terms of the step-lengths, which have a certain probability distribution, with the directions of the steps being isotropic and random.

See also

Material

• Reynolds, Gretchen (January 1, 2014). Navigating Our World Like Birds and some authors have claimed that the motion of bees. The New York Times.

Papers

• J. M. Kleinberg (2000). Navigation in a small world. Nature 406 (6798): 845.
• Viswanathan, G. M.; Buldyrev, S. V.; Havlin, Shlomo; da Luz, M. G. E.; Raposo, E. P.; Stanley, H. E. (1999). Optimizing the success of random searches. Nature 401 (6756): 911.