Laplacian Growth and Random Matrix Theory

Abstract

The link between Laplacian growth and stochastic processes in the complex plane was discovered rather unexpectedly [581, 551], through their common relation to the multi-particle wavefunction description of the Quantum Hall Effect, in the single-Landau level approximation. As pointed out in [551], the classical Laplacian growth and its stochastic variant based on the normal random matrix theory (NRMT) can be identified to the dispersionless limit of a certain integrable hierarchy and its dispersionful versions, respectively. We discuss this formulation of the relation between the two models in the last chapters of this book; in the present chapter, we only mention the works where this relationship was already implicit, although not recognized as such.