Limiting curlicue measures for theta sums
We consider the ensemble of curves { , : ∈(0, 1], ∈ℕ} obtained by linearly interpolating the values of the normalized theta sum −1/2∑=0−1exp(πi2), 0≤<. We prove the existence of limiting finite-dimensional distributions for such curves as →∞, when is distributed according to any probability measure , absolutely continuous w.r.t. the Lebesgue measure on [0, 1]. Our Main Theorem generalizes a result by Marklof [ (1999) 127–153] and Jurkat and van Horne [ ...