Sparse localization deduces entropic independence from sparse ℓ2-independence with explicit loss, yielding approximate entropy conservation for uniform independent sets of fixed size in bounded-degree graphs.
En- tropic independence ii: optimal sampling and concentratio n via restricted modified log- sobolev inequalities
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Under local spectral assumptions from Gur et al., the sequential sweep on high-dimensional expanders has spectral gap near 1 and satisfies entropy contraction, generalizing rapid mixing results from Ramanujan complexes.
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Entropic independence via sparse localization
Sparse localization deduces entropic independence from sparse ℓ2-independence with explicit loss, yielding approximate entropy conservation for uniform independent sets of fixed size in bounded-degree graphs.