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Lalley","submitted_at":"2011-11-08T21:17:51Z","abstract_excerpt":"Let $\\Upsilon $ be a compact, negatively curved surface. From the (finite) set of all closed geodesics on $\\Upsilon$ of length $\\leq L$, choose one, say $\\gamma_{L}$, at random and let $N (\\gamma_{L})$ be the number of its self-intersections. It is known that there is a positive constant $\\kappa$ depending on the metric such that $N (\\gamma_{L})/L^{2} \\rightarrow \\kappa$ in probability as $L\\rightarrow \\infty$. The main results of this paper concern the size of typical fluctuations of $N (\\gamma_{L})$ about $\\kappa L^{2}$. 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