A more general central limit theorem for m-dependent random variables with unbounded m

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The distribution of the zeros of random trigonometric polynomials (2008, methodology): “K converges weakly to N(0,1). 18 ANDREW GRANVILLE AND IGOR WIGMAN Note that condition 4 requires, in particular, that as N → ∞, one has K→ ∞. Berk’s result was recently generalized by Romano and Wolf [RW]. 4.3. Plan of the proof of Theorem 1.1. We deﬁne the scaled processes YN(x) := XN x m , on [0”