Random Z-homomorphisms on weak expanders are O(log log n)-flat with high probability, answering a question of Peled-Samotij-Yehudayoff, and at most 5-valued on Hamming-cube middle layers.
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An asymptotic expansion is derived for the expected number of independent sets in percolated regular bipartite graphs via the Ising model and cluster expansion, extending prior hypercube work.
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Range of random $\mathbb Z$-homomorphisms on weak expanders
Random Z-homomorphisms on weak expanders are O(log log n)-flat with high probability, answering a question of Peled-Samotij-Yehudayoff, and at most 5-valued on Hamming-cube middle layers.