Marginal Distribution weight:w()=A(u).() (u,v)∈E w(o) Gibbs measure: L()=ZA(G) Z4(G)=∑ ΠA(w,o) o∈{0,1V(u,w)∈E marginal distributions at vertex v: p=Pr [o(v)=0] ΛCVoA∈{0,1}A fixed v∈A free vA Pr [o(v)=01(A)=OA]Marginal Distribution weight: w(￾) = ￾ (u,v)￾E A￾(u),￾(v) Gibbs measure: µ(￾) = w(￾) ZA(G) ZA(G) = ￾ ￾￾{0,1}V ￾ (u,v)￾E A￾(u),￾(v) pv = 8Z ￾￾µ [￾(v) = 0] p￾￾ v = 8Z ￾￾µ [￾(v) = 0 | ￾(￾) = ￾￾] ￾￾ ￾ {0, 1}￾ marginal distributions at vertex v: ￾ ￾ V fixed v ￾ ￾ free v ￾￾ ￾