Favard-length decay exponent

Upper bound, last-listed row

| $1$ | [BV2010] | Bateman–Volberg prove $\mathrm{Fav}(K_n)\ge c\,\frac{\log n}{n}$, which rules out any estimate $\mathrm{Fav}(K_n)\le C n^{-\alpha}$ with $\alpha>1$. [BV2010-thm1-lb-logn-over-n] |

exact pinned row

| $1$ | <a href="#BV2010">[BV2010]</a> | Bateman–Volberg prove $\mathrm{Fav}(K_n)\ge c\,\frac{\log n}{n}$, which rules out any estimate $\mathrm{Fav}(K_n)\le C n^{-\alpha}$ with $\alpha>1$. <a href="#BV2010-thm1-lb-logn-over-n">[BV2010-thm1-lb-logn-over-n]</a> |

tracked since 2026-07-24 — no movement seen yet

Lower bound, last-listed row

| $1/6$ | [NPV2011] | Nazarov–Peres–Volberg prove $\mathrm{Fav}(K_n)\le C n^{-1/6+\delta}$ (equivalently, $\mathrm{Fav}(K_n)\le C n^{\delta-1/6}$) for every $\delta>0$. [NPV2011-thm1-powerlaw] |

exact pinned row

| $1/6$ | <a href="#NPV2011">[NPV2011]</a> | Nazarov–Peres–Volberg prove $\mathrm{Fav}(K_n)\le C n^{-1/6+\delta}$ (equivalently, $\mathrm{Fav}(K_n)\le C n^{\delta-1/6}$) for every $\delta>0$. <a href="#NPV2011-thm1-powerlaw">[NPV2011-thm1-powerlaw]</a> |

tracked since 2026-07-24 — no movement seen yet