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arXiv · 1109.4901

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

S. G. Alves·T. J. Oliveira·S. C. Ferreira
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Abstract

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.

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S. G. Alves, T. J. Oliveira, S. C. Ferreira. 2011-09-22. Universal fluctuations in radial growth models belonging to the KPZ universality class. https://doi.org/10.1209/0295-5075%2F96%2F48003

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