Correlation Decay strong spatial mixing(SSM):VoB E[a]5 Pr(a(e)=cA)-Pr(o(e)=cA,OB) ≤poly(IVI)exp(-2(t) SSM:sufficiency of local information for approx.of Pr((e)=cA) efficiency of local computation (FPTAS) such implication was known for: g-2,F is Spin (Weitz6) Matching (Bayati-Gamarnik-Katz-Nair-Tetali'08)Correlation Decay strong spatial mixing (SSM): SSM: sufficiency of local information B G e t A ￾ XWTa(|V |) M`X(￾￾(t)) ￾￾B ￾ [q] B ? for approx. of efficiency of local computation 8Z(￾(e) = c | ￾A) q=2, is F Spin (Weitz’06) Matching (Bayati-Gamarnik-Katz-Nair-Tetali’08) ￾ such implication was known for: (FPTAS) ￾ ￾8Z(￾(e) = c | ￾A) ￾ 8Z(￾(e) = c | ￾A, ￾B) ￾ ￾