APPLICATIONS OF THE FIRST DIGIT LAW TO MEASURE CORRELATIONS
The quasi-empirical Benford law predicts that the distribution of the first significant digit of random numbers obtained from mixed probability distributions is surprisingly meaningful and reveals some universal behavior. We generalize this finding to examine the joint first-digit probability of a pair of two random numbers and show that undetectable correlations by means of the usual covariance-based measure can be identified in the statistics of the corresponding first digits. We illustrate this new measure by analyzing the correlations and anti-correlations of the positions of two interacting particles in their quantum mechanical ground state. This suggests that by using this new measure, the presence or absence of correlations can be determined even if only the first digit of noisy experimental data can be measured accurately.  This work has been supported by the NSF, NSFC and Research Corporation.  R. Gramm, J. Yost, Q. Su and R. Grobe, Phys. Rev. E 95 042136 (2017).
Yost, Jack, "APPLICATIONS OF THE FIRST DIGIT LAW TO MEASURE CORRELATIONS" (2019). University Research Symposium. 354.