Transition function

In mathematics, a transition function has several different meanings:

• In topology and in particular in the theory of manifolds, a transition function between two charts of an atlas is a map which allows to pass from one chart to the other in the region where they intersect.

• In computing, a transition function is the function that defines the state transitions of a Turing machine, finite-state machine, or cellular automaton.

• In statistics and probability theory, a transition function is a stochastic kernel, the conditional probability distribution function controlling the transitions of a stochastic process.

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