Random Points on an Algebraic Manifold
Paul Breiding, Orlando Marigliano · SIAM Journal on Mathematics of Data Science · 2020
Consider the set of solutions to a system of polynomial equations in many variables. An algebraic manifold is an open submanifold of such a set. We introduce a new method for computing integrals and sampling from distributions on algebraic manifolds. This method is based on intersecting with random linear spaces. It produces independent and identically distributed samples, works in the presence of multiple connected components, and is simple to implement. We present applications to computational statistical physics and topological data analysis.