Abstract
We prove that the Airy process, $\mathscr{A}(t)$, locally fluctuates like a Brownian motion. In the same spirit we also show that, in a certain scaling limit, the so-called discrete polynuclear growth process (PNG) behaves like a Brownian motion.
Citation
Jonas Hägg. "Local Gaussian fluctuations in the Airy and discrete PNG processes." Ann. Probab. 36 (3) 1059 - 1092, May 2008. https://doi.org/10.1214/07-AOP353
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