Mathematics Colloquium by Nathan Szeto ’23

To Accept or Reject, That is the Question: An Application of the Rejection Method to the Circular Beta Ensemble by Nathan Szeto ’23, Mathematics Colloquium, Tuesday, May 16, 1 – 1:40 pm, North Science Building 113, Wachenheim.

Abstract:  The Circular Beta Ensemble is a point process used to model the distribution of particles confined to a one-dimensional space at various temperatures T = 1/beta. We sample from this distribution using the accept-reject sampling method, or the rejection method.  We verify mathematically that this method can be applied to distributions of multiple, mutually dependent variables.  We then proceed to a discussion of the empirical supremum rejection sampling method, which is a modified version of the rejection method that results in faster sampling runtimes through iterative improvements to the selected value of a specific parameter.  We prove the validity of this method mathematically and proceed to implement it in R to demonstrate improved runtimes.