The full edge scaling limit of singular values of GL_N(C) Brownian motion solves an infinite log-interacting SDE system, and the limiting reverse characteristic polynomial satisfies a nonlinear multiplicative-noise SPDE.
From integrable to chaotic systems: Universal local statistics of lyapunov exponents.Europhysics Letters 126, 4 (2019), 40001
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$\mathsf{GL}_N(\mathbb{C})$ Brownian motion and stochastic PDE on entire functions
The full edge scaling limit of singular values of GL_N(C) Brownian motion solves an infinite log-interacting SDE system, and the limiting reverse characteristic polynomial satisfies a nonlinear multiplicative-noise SPDE.