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.
A simple condition implying rapid mi xing of single-site dynamics on spin systems
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Sequential Sweeps and High Dimensional Expansion
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.