"Infinite-dimensional stochastic differential equations arising from Airy random point fields",
We identify infinite-dimensional stochastic differential equations (ISDEs) describing the stochastic dynamics related to Airy random point fields with =1,2,4. We prove the existence of unique strong solutions of these ISDEs. When =2, this solution is equal to the stochastic dynamics defined by the space-time correlation functions obtained by Spohn and Johansson among others. We develop a new method to construct a unique, strong solution of ISDEs. We expect that our approach is valid for other soft-edge scaling limits of stochastic dynamics arising from the random matrix theory.
