At time zero, the real line is partitioned into intervals. The original partition, which may be random, evolves according to a deterministic rule whereby the interface between consecutive pair of cells moves so as to make the larger cell grow and the smaller cell shrink. This is a somewhat degenerate one-dimensional version of a two (and higher) dimensional mean-curvature flow model about which almost nothing rigorous is known. We show that the Poisson measure is invariant for this evolution, provided that space is rescaled exponentially. We do this by introducing the dual process (time-reversal). This process, unlike the forward process, contains some randomness and may be exactly analyzed.

JOINT WORK WITH EMANUEL LAZAR