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We consider the Kardar-Parisi-Zhang (KPZ) equation for a circular interfacein two dimensions, unconstrained by the standard small-slopes and no-overhangapproximations. Numerical simulations using an adaptive scheme allow us toelucidate the complete time evolution as a crossover between a short-timeregime with the interface fluctuations of a self-avoiding ring or 2D vesicle,and a long-time regime governed by the Tracy-Widom distribution expected forthis geometry. For small noise amplitudes, scaling behavior is only of thelatter type. Large noise is also seen to renormalize the bare physicalparameters of the ring, akin to analogous parameter renormalization forequilibrium 3D membranes. Our results bear particular importance on therelation between relevant universality classes of scale-invariant systems intwo dimensions.

The circular Kardar-Parisi-Zhang equation as an inflating, self-avoiding ring polymer