Random points on an algebraic manifold
Abstract
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 i.i.d. 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2018
 arXiv:
 arXiv:1810.06271
 Bibcode:
 2018arXiv181006271B
 Keywords:

 Mathematics  Algebraic Geometry