Thus K p,q (X; L d ) is a finite-dimensional vector space, and E p (X; L d ) = q K p,q (X; L d ) ⊗ k S(−p − q).We refer to an element of K p,q as a p th syzygy of weight q. The dimensionsare the Betti numbers of L d ; they are the entries of the Betti table of L d . The basic problem motivating the present paper (one that alas we do not solve) is to understand the asymptotic behavior of these numbers as d → ∞.Elementary considerations of Castelnuovo-Mumford regularity show that if d 0 thenThe main result of [5] is that as d → ∞ these groups become nonzero for "essentially all" values of the parameters. Specifically, there exist constants C 1 , C 2 > 0 (depending on X and the choice of the divisors A, P appearing in the definition of L d ) such that if one fixes 1 ≤ q ≤ n, then K p,q (X; L d ) = 0 for every value of p satisfyingHowever the results of [5] do not say anything quantitative about the asymptotics in p of the corresponding Betti numbers k p,q (X; L d ) for fixed weight q ∈ [1, n] and d 0.The question is already interesting in the case n = 1 of curves: here it is only the k p,1 that come asymptotically into play. 1 Figure 1 shows plots of these Betti numbers for a divisor of degree 75 on a curve of genus 0, and on a curve of genus 10. The figure suggests that the k p,1 become normally distributed, and we prove that this is indeed the case: Proposition A. Let L d be a divisor of large degree d on a smooth projective curve X of genus g, so that r d = d − g. Choose a sequence {p d } of integers such that