=+Now define the neighborhoods N so that X is independent of those X with outside N.

=+Now define the neighborhoods Nα so that Xα is independent of those Xβ with β outside Nα. Demonstrate that



α∈I



β∈Nα

pαpβ =

n d

 n d



−

n − d d

  1 m

2d−2



α∈I



β∈Nα\{α}

pαβ =

n d

 d

−1 i=1

d i

n − d d − i

  1 m

2d−i−1

.

When d = 2, calculate the total variation bound

πS − πZTV ≤

1 − e−λ

λ

n 2

(4n − 7)

m2 .