Abstract
We use a mathematical isomorphism between the one-dimensional exclusion process and the two-dimensional stochastic Ising model in the low-temperature limit to describe the typical instantaneous shape of a supercritical droplet. We derive, specifically, the exact asymptotic distribution of the boundaries of a (+1) spin region, confined to Z + 2 and subjected to a positive magnetic field. In an appropriate scaling, the boundary distribution converges to a deterministic continuum limit.
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