Spatial Mixing weak spatial mixing (WSM): Pr[c(w)=x|o△]≈Pr[C(v)=x|TA] strong spatial mixing (SSM): Pr[c(v)=A,]Pr[c(v)=xTA,OA] error exp (-t) SSM:the value of critical to Pr[c(v)=O] counting and sampling is approximable by local informationSpatial Mixing R G v t ⇤ weak spatial mixing (WSM): strong spatial mixing (SSM): error < exp (-t) Pr[c(v) = x | ￾⇤] is approximable by local information SSM: the value of critical to counting and sampling Pr[c(v) = x | ￾￾] ⇡ Pr[c(v) = x | ⌧￾] Pr[c(v) = x | ￾￾, ￾⇤] ⇡ Pr[c(v) = x | ⌧￾, ￾⇤] ∆