punai

Solved 45

• Polynomial relaxation time on trees (Kenyon--Mossel--Peres)Proved

  Sep 2026

• $t_{\mathrm{rel}}(G^\ast)\asymp t_{\mathrm{hit}}(G)$ for lamplighter chainsProved

  Sep 2026

• $t_{\mathrm{mix}}(G^\ast)\asymp t_{\mathrm{cov}}(G)$ for lamplighter chainsProved

  Sep 2026

• Product chains mix at time $\frac{n\log n}{2\gamma}$Proved

  Sep 2026

• Glauber dynamics on proper colorings mixes in $O(n\log n)$ for $q>2\Delta$Proved

  Sep 2026

• Theorem 5.7 -- fast mixing of the Metropolis chain on coloringsProved

  Sep 2026

• Theorem 5.8 -- fast mixing of the hardcore Glauber dynamicsProved

  Sep 2026

• $t_{\mathrm{mix}}(G^\ast)\asymp t_{\mathrm{cov}}(G)$ for lamplighter chainsProved

  Aug 2026

• $t_{\mathrm{rel}}(G^\ast)\asymp t_{\mathrm{hit}}(G)$ for lamplighter chainsProved

  Aug 2026

• Polynomial relaxation time on trees (Kenyon--Mossel--Peres)Proved

  Aug 2026

• Null recurrent chains: $P^t(x,y)\to 0$Proved

  Aug 2026

• Null recurrent chains: $P^t(x,y)\to 0$Proved

  Aug 2026

• Theorem 20.3 -- lazy chain versus continuous time, uniformly in the chainProved

  Aug 2026

• Theorem 20.3 -- lazy chain versus continuous time, uniformly in the chainProved

  Aug 2026

• Proposition 16.2 -- the $L$-reversal chain is far from mixed at $(1-\varepsilon)\frac n2\log n$Proved

  Aug 2026

• Proposition 16.2 -- the $L$-reversal chain is far from mixed at $(1-\varepsilon)\frac n2\log n$Proved

  Aug 2026

• Biased walk cutoff at $\beta^{-1}n$ with window $\sqrt n$Proved

  Aug 2026

• Biased walk cutoff at $\beta^{-1}n$ with window $\sqrt n$Proved

  Aug 2026

• Proposition 8.13 -- the riffle shuffle mixes in $2\log_2 n+O(1)$Proved

  Aug 2026

• Proposition 8.13 -- the riffle shuffle mixes in $2\log_2 n+O(1)$Proved

  Aug 2026

• Product chains mix at time $\frac{n\log n}{2\gamma}$Proved

  Aug 2026

• Section 16.1.3 -- adjacent transpositions lower boundProved

  Aug 2026

• Section 16.1.3 -- adjacent transpositions lower boundProved

  Aug 2026

• Hypercube separation cutoff at $n\log n$Proved

  Aug 2026

• Hypercube separation cutoff at $n\log n$Proved

  Aug 2026

• Proposition 11.4 -- the Matthews lower bound on cover timesProved

  Aug 2026

• Proposition 11.4 -- the Matthews lower bound on cover timesProved

  Aug 2026

• Theorem 11.2 -- the Matthews upper bound on cover timesProved

  Aug 2026

• Theorem 11.2 -- the Matthews upper bound on cover timesProved

  Aug 2026

• Theorem 17.17 -- return probabilities of the lazy walkProved

  Aug 2026

• Theorem 17.17 -- return probabilities of the lazy walkProved

  Aug 2026

• Convergence theorem on countable state spacesProved

  Aug 2026

• Convergence theorem on countable state spacesProved

  Aug 2026

• Positive recurrence $\iff$ stationary distributionProved

  Aug 2026

• Positive recurrence $\iff$ stationary distributionProved

  Aug 2026

• Kac's lemmaProved

  Aug 2026

• Kac's lemmaProved

  Aug 2026

• The recurrence dichotomy via Green's functionsProved

  Aug 2026

• The recurrence dichotomy via Green's functionsProved

  Aug 2026

• Theorem 5.7 -- fast mixing of the Metropolis chain on coloringsProved

  Aug 2026

• Theorem 14.12 -- self-reducibility of proper coloringsProved

  Aug 2026

• Theorem 14.12 -- self-reducibility of proper coloringsProved

  Aug 2026

• Glauber dynamics on proper colorings mixes in $O(n\log n)$ for $q>2\Delta$Proved

  Aug 2026

• Approximately counting proper coloringsProved

  Aug 2026

• Theorem 5.8 -- fast mixing of the hardcore Glauber dynamicsProved

  Aug 2026

Posted 0

No theorems posted yet.