In probability theory and its applications, such as statistics and cryptography, a random function is a function chosen randomly from a family of possible functions. Each realisation of a random function would result in a different function. Thus the concept of a random function is one example of a random element and hence is a generalization of the simpler idea of a random variable.
In probability and statistics, one important type of random function is studied under the name of stochastic processes, for which there are a variety of models describing systems where an observation is a random function of time or space. However, there are other applications where there is a need to describe the uncertainty with which a function is known and where the state of knowledge about the true function can be expressed by saying that it is an unknown realisation of a random function, for example in the Dirichlet process.
A special case of a random function is a random permutation, where a realisation can be interpreted as being in the form of a function on the set of integers describing the original location of an item, where the value of the function provides the new (permuted) location of the item that was in a given location.
In cryptography, a random function can be a useful building block in enabling cryptographic protocols.
Read more about Random Function: Definition, Applications
Famous quotes containing the words random and/or function:
“There is a potential 4-6 percentage point net gain for the President [George Bush] by replacing Dan Quayle on the ticket with someone of neutral stature.”
—Mary Matalin, U.S. Republican political advisor, author, and James Carville b. 1946, U.S. Democratic political advisor, author. All’s Fair: Love, War, and Running for President, p. 205, Random House (1994)
“As a medium of exchange,... worrying regulates intimacy, and it is often an appropriate response to ordinary demands that begin to feel excessive. But from a modernized Freudian view, worrying—as a reflex response to demand—never puts the self or the objects of its interest into question, and that is precisely its function in psychic life. It domesticates self-doubt.”
—Adam Phillips, British child psychoanalyst. “Worrying and Its Discontents,” in On Kissing, Tickling, and Being Bored, p. 58, Harvard University Press (1993)