Correlation Decay weak spatial mixing (WSM): oaB,TaB∈{0,1}B |Pr((v)=0|08B)-Pr(a(v)=0 TaB)I<exp(-S(t)) strong spatial mixing (SSM): Pr((v)=0 00B,n)-Pr(G(v)=0 TOB,A)I<exp(-2(t)) G Uniqueness: WSM in reg.treeCorrelation Decay strong spatial mixing (SSM): B ￾B G v ￾￾￾B, ￾￾B ￾ {0, 1}￾B ￾ t weak spatial mixing (WSM): Uniqueness: WSM in reg. tree | 8Z(￾(v) = 0 | ￾￾B) ￾ 8Z(￾(v) = 0 | ￾￾B)| ￾ M`X(￾￾(t)) | 8Z(￾(v) = 0 | ￾￾B, ￾￾) ￾ 8Z(￾(v) = 0 | ￾￾B, ￾￾)| ￾ M`X(￾￾(t))