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.
[JPS26] Matthew Jenssen, Jinyoung Park, and Michail Sarantis
3 Pith papers cite this work. Polarity classification is still indexing.
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Monte Carlo layer-ratio reconstruction via fixed-layer Markov chains produces the estimate M(10) ≈ 8.936 × 10^78 with uncertainty from cross-n scaling calibrated on known smaller values.
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.
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Finite-n Estimate of Dedekind Numbers by Layer-Ratio Monte Carlo
Monte Carlo layer-ratio reconstruction via fixed-layer Markov chains produces the estimate M(10) ≈ 8.936 × 10^78 with uncertainty from cross-n scaling calibrated on known smaller values.
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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.