Main Result g=ad+B for a>2 and some B=0(1)(23 is enough) fix any vE[n],and then sample G(n,d/n) whp:G(n,d/n)is g-colorable,and for any o,T Pr[c(v)=x o]-Pr[c(v)=xT=exp(-(t)) t=dist(v,△)=w(1) is the shortest distance from v to where o,t differ Strong Spatial Mixing w.r.t any fixed vertex!Main Result R G v t ⇤ q ≥ αd + β for α>2 and some β=O(1) (23 is enough) fix any v∈[n], and then sample G(n,d/n) whp: G(n,d/n) is q-colorable, and for any ￾, ⌧ is the shortest distance from v to where σ,τ differ Strong Spatial Mixing w.r.t any fixed vertex! |Pr[c(v) = x | ￾] ￾ Pr[c(v) = x | ⌧ ]| = exp (￾⌦(t)) ∆ t = dist(v, ￾) = !(1)