Limiting Curlicue Measures for Theta Sums

Mathematics – Dynamical Systems

Scientific paper

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36 pages, 3 figures, submitted to Ann. Inst. Henri Poincare' Probab. Stat

Scientific paper

We consider the ensemble of curves $\{\gamma_{\alpha,N}:\alpha\in(0,1],N\in\N\}$ obtained by linearly interpolating the values of the normalized theta sum $N^{-1/2}\sum_{n=0}^{N'-1}\exp(\pi i n^2\alpha)$, $0\leq N'

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