KPZ Fluctuations of Sticky Brownian Motion

Sticky Brownian motion is a type of diffusion consisting of many interacting particles, where each individual particle behaves as standard Brownian motion but collectively the different particles may stick together and separate repeatedly. The sticky interaction makes the system physically interesting and difficult to study. We show that a singular stochastic SPDE called the KPZ equation arises as the fluctuations limit of a large number of sticky Brownian particles in the moderate deviation regime.

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