Local Gaussian fluctuations in the Airy and discrete PNG processes

Abstract

We prove that the Airy process, 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 (PNG) process behaves like a Brownian motion.

34 pages

References in corpus (3)

• Discrete polynuclear growth and determinantal processes
• On Asymptotics for the Airy Process
• A PDE for the joint distributions of the Airy Process