Conference Proposal: Theory and Applications of Benford's Law

Brown University, Providence RI

Investigators

Abstract

Benford's Law describes the distribution of the leading significant digit of many data sets; rather than being uniformly distributed, the probability the first digit equals d is often log_10(1 + 1/d). The number of systems satisfying Benford's Law is astounding, and extremely diverse, including budget and income tax data, stock market tables, census figures, DCT-domain coefficients in images, hydrology data, standard mathematical functions (such as n!), iterates of dynamical maps, values of L-functions and characteristic polynomials of random matrix ensembles, solutions of recurrence relations, and the 3x+1 problem, to name just a few. We believe that our proposed workshop is the first attempt to assemble a large, representative sample of people in the myriad of disciplines working on the theory and applications of Benford's law. There are numerous examples of major advances in science and mathematics arising from people applying the tools and techniques of one field in another. We hope to have similar success here. Specifically, by gathering experts from all the different fields studying Benford's law, we plan on disseminating the problems and techniques across the different disciplines. It is likely that participants will be able to provide helpful suggestions to each other (or be intrigued by proposed questions and participate in joint research). The list of topics include mathematical foundations, interpretation, information forensics and fraud detection, signal and data processing, dynamical systems, complex networks and system design. As one of our primary goals is to disseminate knowledge of tools, techniques and problems related to Benford's Law throughout the community, we plan on publishing proceedings of the workshop. We are investigating the publication through SIAM or AMS of a book based on the workshop talks, as well as possibly some expository articles. The immediate deliverables of the workshop will be a report, as well as electronic proceedings. The longer term deliverables are published proceedings as well as a team proposal for a large grant.