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Convex cones, integral zonotopes, limit shapes

by · Jul 23, 2016 · 373 views ·

Given a pointed cone CC in RdRd, an integral zonotope in CC is the Minkowski sum of segments of the form [0,zi][0,zi] (i=1,…,m)(i=1,…,m) where zizi is an integer vector from CC. The endpoint of this zonotope is the sum of the zizi. The collection T(C,k)T(C,k) of integral polytopes in CC with endpoint kk is a finite set. We show that the zonotopes in T(C,k)T(C,k) have a limit shape as kk goes to infinity. The proofs combine geometry and probability theory. Several new (and exciting) questions have emerged. Joint work with Julien Bureaux and Ben Lund.

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