We study limiting behavior of rescaled size distributions in
several models of clustering or coagulation dynamics, `solvable'
in the sense that the Laplace transform converts them into
nonlinear PDE. The scaling analysis that emerges has many
connections with the classical limit theorems of probability
theory, and an application to the study of shock clustering in
the inviscid Burgers equation with random-walk initial data.
I'll focus on recent progress regarding a `min-driven' clustering
model related to domain coarsening dynamics in the Allen-Cahn
equation.
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