The Complexity of Distributions

Complexity theory, with some notable exceptions, typically studies the complexity of computing a function h(x) of a *given* input x. We advocate the study of the complexity of generating -- or sampling -- the output distribution h(x) for random x, given random bits.

In particular, we present first-of-their-kind lower bounds for generating distributions in various restricted computational models. We also discuss connections to succinct data structures and to randomness extractors.