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 Universal fluctuations in radial growth models belonging to the KPZ universality class


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We investigate the radius distributions RD of surfaces obtained with large-scale simulations of radial clusters that belong to the KPZ universality class. For all investigated models, the RDs are given by the Tracy-Widom distribution of the Gaussian unitary ensemble, in agreement with the conjecture of the KPZ universality class for curved surfaces. The quantitative agreement was also confirmed by two-point correlation functions asymptotically given by the covariance of the Airy$ 2$ process. Our simulation results fill the last lacking gap of the conjecture that had been recently verified analytically and experimentally.



Author: S. G. Alves; T. J. Oliveira; S. C. Ferreira

Source: https://archive.org/



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