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

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

2011-09-22

arxiv.org/abs/1109.4901v1

Europhysics Letters 96 (2011) 48003

Physics

Condensed Matter

Statistical Mechanics

5 pages, 5 figures

Scientific paper

10.1209/0295-5075/96/48003

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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