Heuristically, two processes are dual if one can find a function to study one process by using the other. Sampling duality is a duality which uses a duality function S(n,x) of the form "what is the probability that all the members of a sample of size n are of a certain type, given that the number (or frequency) of that type of individuals is x". Implicitly, this technique can be traced back to the work of Blaise Pascal. Explicitly, it was studied in a paper of Martin Möhle in 1999 in the context of population genetics. We will discuss examples for which this technique is useful, including an application to the Simple Exclusion Process with reservoirs. The last part of the lecture is based in recent joint work with Simone Floriani https://arxiv.org/abs/2307.02481

### Probability and Combinatorics

Tuesday, October 17, 2023 - 3:30pm

#### Adrián González-Casanova

University of California, Berkeley