Random Number Generation Using Normal Numbers

Normal numbers are irrationals with perfect digit distribution, and thus they are potentially sources of computational random numbers. Among provably normal numbers are the Stoneham numbers, which are special not only in their digit distribution, but in the fact that finite segments of the digits can be quickly computed. Thus, we examine random numbers produced by periodic sections of the digits of Stoneham numbers. We show how they are equivalent to a linear congruential generator with special parameters, and we investigate this generator as a linear congruential generator. This is joint work with Steve F. Brailsford.

Speaker Bio: Michael Mascagni is an internationally recognized expert on all aspects of random number generation and Monte Carlo methods, and has lectured extensively across the globe. He received his undergraduate degrees in Biomedical Engineering and Mathematics at the University of Iowa in 1981, and entered Rockefeller University to study neurobiology. While taking some math courses at NYU he decided to switch to math, and he moved to the Courant Institute in 1983. He graduated in 1987, having worked with Prof. Charlie Peskin on the numerical solution of nerve equations. He then did a post-doc at NIH and worked for many years with the Institute for Defense Analyses. He reentered academia, and in 1999 moved to Florida State University's Computer Science Department. He has published over 100 scholarly articles, has graduated doctoral students in Computer Science, Mathematics, and Scientific Computing, and he currently leads a research group working in high-performance computing aspects of Monte Carlo methods and random number generation. He has been a visiting faculty member at Universite' de Toulon et du Var, Universit\"{a}t Salzburg, Universit\"{a}t Kaiserslautern, and Universita` degli Studi di Padova. He also spent a sabbatical year visiting the Seminar f\"{u}r Angewandte Mathematik, Departement Mathematik, Eidgenössische Technische Hochschule (ETH-Z\"{u}rich). He was elected an Association for Computing Machinery (ACM) Distinguished Scientist in 2011, and is currently a Faculty Appointee at the National Institute of Standards and Technology (NIST).

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