Consider a two-dimensional lattice with vertices v = (i, j); i, j = 1,2, .... To each
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Consider a two-dimensional lattice with vertices v = (i, j); i, j = 1,2, .... To each vertex v, we assign a r.v. ξv and assume ξ’s to be i.i.d. A neighborhood Nv consists of the nearest vertices. Let Xv = ξv · Πu∈Nv ξu (the product of the r.v.’s in the neighborhood). State the CLT for the case where ξ’s are uniform on [−1,1].
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