This intuition was used by Perelman.

Quote from Tao: “We now come to an interesting (but still mostly heuristic) correspondence principle between elliptic theory and parabolic theory, with the latter being viewed as an infinite-dimensional limit of the former, in a manner somewhat analogous to that of the central limit theorem in probability”

References: “Parabolic theory as a high-dimensional limit of elliptic theory”

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