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- W4300762064 abstract "We determine the leading digit laws for the matrix components of a linear Lie group $G$. These laws generalize the observations that the normalized Haar measure of the Lie group $mathbb{R}^+$ is $dx/x$ and that the scale invariance of $dx/x$ implies the distribution of the digits follow Benford's law, which is the probability of observing a significand base $B$ of at most $s$ is $log_B(s)$; thus the first digit is $d$ with probability $log_B(1 + 1/d)$). Viewing this scale invariance as left invariance of Haar measure, we determine the power laws in significands from one matrix component of various such $G$. We also determine the leading digit distribution of a fixed number of components of a unit sphere, and find periodic behavior when the dimension of the sphere tends to infinity in a certain progression." @default.
- W4300762064 created "2022-10-04" @default.
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- W4300762064 date "2015-07-06" @default.
- W4300762064 modified "2023-10-16" @default.
- W4300762064 title "Leading Digit Laws on Linear Lie Groups" @default.
- W4300762064 doi "https://doi.org/10.48550/arxiv.1507.01605" @default.
- W4300762064 hasPublicationYear "2015" @default.
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