Lacunarity exponents

Wilkinson, Michael; Pradas, Marc; Huber, Greg and Pumir, Alain (2019). Lacunarity exponents. Journal of Physics A: Mathematical and Theoretical, 52(11), article no. 115101.



Many physical processes result in very uneven, apparently random, distributions of matter, characterised by fluctuations of the local density varying over orders of magnitude. The density of matter in the sparsest regions can have a powerlaw distribution, with an exponent that we term the lacunarity exponent. We discuss a mechanism which explains the wide occurrence of these power laws, and give analytical expressions for the exponent in some simple models.

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