Consider a two-dimensional lattice with vertices v = (i, j); i, j = 1,2, .... To each vertex v, we assign a r.v. v

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