Generation of discrete random variables in scalable framework

In this paper, we face the problem of simulating discrete random variables with general and varying distribution in a scalable framework, where fully parallelizable operations should be preferred. Compared with classical algorithms, we add randomness, that will be analyzed with a fully parallelizable operation, and we leave the final simulation of the random variable to a single associative operator. We characterize the set of algorithms that work in this way, and some classes of them related to an additive or multiplicative local noise. As a consequence, we could define a natural way to solve some popular simulation problems.