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.
Independent sets in the discrete hypercube
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
abstract
In this expository note we describe a proof due to A. Sapozhenko that the number of independent sets in the discrete $d$-dimensional hypercube $Q_d$ is asymptotically $2 \sqrt{e} 2^{2^{d-1}}$ as $d$ tends to infinity.
citation-role summary
background 1
citation-polarity summary
fields
math.CO 2verdicts
UNVERDICTED 2roles
background 1polarities
background 1representative citing papers
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.
citing papers explorer
-
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.
-
Counting independent sets in percolated graphs via the Ising model
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.