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I will discuss recent work regarding a simple model for adding cubes to a pile, with the constraint that the pile never have a step of size greater than one. If a newly added cube would violate this condition, it randomly ``falls downhill", coming to rest in a position that keeps the constraint. If we randomly add more and more, smaller and smaller cubes, we obtain an interesting continuum limit, which is an evolution governed by the subdifferential of a convex functional. I will explain as well the connections with Monge-Kantorovich theory.
This is joint work with F. Rezakhanlou.
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