Aldous spectral gap theorem
= Aldous spectral gap theorem
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On a finite connected weighted <graph>, the <interchange process> and the single-label <random walk> with the same symmetric rates have equal <spectral gaps>. This is a substantial theorem, not just the elementary inclusion of the single-label <spectrum> in the full <spectrum>. A proof is given in https://arxiv.org/abs/0906.1238[Proof of Aldous' spectral gap conjecture], Theorem 1.1.