Small-Set Expansion in the 2-Degree Short-Code Graph, the Easier Version

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Proves that the degree-2 short-code graph satisfies small-set expansion for d-global sets by giving a Bonami-style hypercontractive bound: the d-degree part of any d‑delta-global function has its 4-norm controlled by its 2-norm, enabling escape probability ≈ 1 − 2^{−r} when r and globality scale like r^2. Uses rank‑1 edge model, Laplacians and coordinate derivatives, recurses on degree, handles dictator (rank‑one) obstructions, and carries the estimate through the short‑code → Grassmann reduction. short-code graph is an SSE for d-global sets Bonami-type hypercontractive bound on d-degree part

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" chapters (10)

1. 0:00Introduction
2. 2:572-to-2 conjecture to short-code graphs
3. 8:28Global sets and noisy mesh counterexample
4. 11:06Sausage property for noisy mesh
5. 14:49Global sets in short-code graph
6. 18:59Hypercontractive estimates and Bonami bounds
7. 29:31Bonami lemma for noisy cube
8. 33:23Degree decomposition and Laplacians
9. 43:41Bounding fourth norm with derivatives
10. 59:48Summary and open questions