Polynomial Time Samplable Distributions

This paper studies the complexity of the polynomial-time samplable (P-samplable) distributions, which can be approximated within an exponentially small factor by sampling algorithms in time polynomial in the length of their outputs. The paper shows that common assumptions in complexity theory yield the separation of polynomial-time samplable distributions from the polynomial-time computable distributions with respect to polynomial domination, average-polynomial domination, polynomial equivalence, and average-polynomial equivalence.