An information scaling law: ζ= 3/4

25 Oct 2017Michael C. AbbottBenjamin B. Machta

Consider the entropy of a unit Gaussian convolved over a discrete set of K points, constrained to an interval of length L. Maximising this entropy fixes K, and we show that this number exhibits a novel scaling law K ~ L^1/\zeta as L -> infinity, with exponent \zeta = 3/4. This law was observed numerically in a recent paper about optimal effective theories; here we present an analytic derivation... (read more)

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