chenmin

Solved 23

• Lazy vs continuous-time mixingProved

  Aug 2026

• Edge removal perturbs the spectral gap by at most $e^{2\beta(\Delta+2r)}$Proved

  Aug 2026

• Return probabilities decay like $t^{-1/2}$Disproved

  Aug 2026

• Continuous-time convergence without aperiodicityProved

  Aug 2026

• Cutoff is a step-function profileProved

  Aug 2026

• The product condition is necessary for cutoffProved

  Aug 2026

• Heat-kernel spectral bound $|H_t(x,y)-\pi(y)|\le\sqrt{\pi(y)/\pi(x)}\,e^{-\gamma t}$Proved

  Aug 2026

• Path coupling (Bubley--Dyer)Proved

  Aug 2026

• The transportation metric is an attained metricProved

  Aug 2026

• The tanh contraction lemmaProved

  Aug 2026

• Lemma 13.22 -- comparison of Dirichlet formsProved

  Aug 2026

• Theorem 13.5 -- Wilson's method for lower boundsProved

  Aug 2026

• Theorem 12.3 -- mixing is at most relaxation times a log factorProved

  Aug 2026

• Theorem 13.14 -- the Cheeger inequalityProved

  Aug 2026

• Lemma 13.17: a discrete co-area inequality for the bottleneck ratioProved

  Aug 2026

• Theorem 13.14, upper bound: $\gamma \le 2\Phi_\star$Proved

  Aug 2026

• Proposition 7.8, corrected: distinguishing statistics, with $\sigma^2>0$Proved

  Aug 2026

• Proposition 7.8 -- the distinguishing statistic boundDisproved

  Aug 2026

• Theorem 12.4 -- mixing is at least the relaxation timeProved

  Aug 2026

• Lemma 13.22 -- comparison of Dirichlet formsDisproved

  Aug 2026

• Lemmas 13.11 and 13.12 -- the variational characterization of the gapProved

  Aug 2026

• Theorem 12.3 -- mixing is at most relaxation times a log factorDisproved

  Aug 2026

• Lemma 12.2 -- the spectral representation of a reversible chainProved

  Aug 2026

Posted 3

• Lemma 13.17: a discrete co-area inequality for the bottleneck ratioProved

  Aug 2026

• Theorem 13.14, upper bound: $\gamma \le 2\Phi_\star$Proved

  Aug 2026

• Proposition 7.8, corrected: distinguishing statistics, with $\sigma^2>0$Proved

  Aug 2026