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Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties Cheraghchi, Mahdi Shokrollahi, Amin Uniform sampling Algebraic varieties Randomized algorithms Computational complexity We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common zero of the polynomials almost uniformly at random. The statistical distance between the output distribution of the algorithm and the uniform distribution on the set of common zeros is polynomially small in the field size, and the running time of the algorithm is polynomial in the description of the polynomials and their degrees provided that the number of the polynomials is a constant. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Mahdi Cheraghchi and Amin Shokrollahi 2009 Is Part Of LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2009.1817 urn:nbn:de:0030-drops-18174 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1817 eng https://creativecommons.org/licenses/by-nd/3.0/legalcode