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math.MG2010★ 2 cited
Nonamenable Liouville Graphs
Itai Benjamini, Gady Kozma
Add to each level of binary tree edges to make the induced graph on the level a uniform expander. It is shown that such a graph admits no non-constant bounded harmonic functions.
math.MG2006★ 2 cited
On the hyperplane conjecture for random convex sets
Bo'az Klartag, Gady Kozma
Let N > n, and denote by K the convex hull of N independent standard gaussian random vectors in an n-dimensional Euclidean space. We prove that with high probability, the isotropic…