LA Probability Forum

Heuristically, two processes are dual if one can find a function that allows studying one process using the other. Sampling duality is a form of duality that employs a function S(n,x), which expresses the probability that all members of a sample of size n are of a certain type, given that the number (or frequency) of that type in the population is x. Implicitly, this technique can be traced back to the work of Blaise Pascal (1623–1662), while it was explicitly formalized in a 1999 paper by Martin Möhle in the context of population genetics.

In this talk, we will explore cases where sampling duality proves useful, including applications in population genetics and a universality result for the Fisher-KPP stochastic partial differential equation.