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- Title
Scale Dependence of Distributions of Hotspots.
- Authors
Wilkinson, Michael; Veytsman, Boris
- Abstract
We consider a random field ϕ (r) in d dimensions which is largely concentrated around small ‘hotspots’, with ‘weights’, w i . These weights may have a very broad distribution, such that their mean does not exist, or is dominated by unusually large values, thus not being a useful estimate. In such cases, the median W ¯ of the total weight W in a region of size R is an informative characterisation of the weights. We define the function F by ln W ¯ = F (ln R) . If F ′ (x) > d , the distribution of hotspots is dominated by the largest weights. In the case where F ′ (x) - d approaches a constant positive value when R → ∞ , the hotspots distribution has a type of scale-invariance which is different from that of fractal sets, and which we term ultradimensional. The form of the function F(x) is determined for a model of diffusion in a random potential.
- Publication
Journal of Statistical Physics, 2024, Vol 191, Issue 5, p1
- ISSN
0022-4715
- Publication type
Article
- DOI
10.1007/s10955-024-03272-1