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:
“Novels as dull as dishwater, with the grease of random sentiments floating on top.”
—Italo Calvino (1923–1985)
“Our father has an even more important function than modeling manhood for us. He is also the authority to let us relax the requirements of the masculine model: if our father accepts us, then that declares us masculine enough to join the company of men. We, in effect, have our diploma in masculinity and can go on to develop other skills.”
—Frank Pittman (20th century)