Gibbs measure undirected graph G=(V,E) configuration o∈[g]V w(o) Gibbs distribution:)=HG()- by the chain rule:denoted V={v1,02,...,vn} w(o) w(o) u(σ)】 IIR=1PrX~uG[Xv:Ov:Vj<i:Xv3 =vj marginal probability:()=Pr[X=Xs=] X~HG where ve∈V,x∈[ql,boundary condition o∈[g]s on SCV approximately computing() FPTAS withinμg(c)±in time Poly(m for ZGGibbs Measure undirected graph G = (V, E) ￾ 2 [q] V configuration Gibbs distribution: by the chain rule: denoted V = {v1, v2,...,vn} where v∈V, x∈[q], boundary condition σ∈[q]S on S⊂V marginal probability: µ￾ v (x) = Pr X⇠µG [Xv = x | XS = ￾] FPTAS for ZG µ￾ v approximately computing (x) within µ￾ v (x) ± 1 n in time Poly(n) µ(￾) = µG(￾) = w(￾) ZG