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Bootstrapping and double-exponential limit laws

Abstract : We provide a rather general asymptotic scheme for combinatorial parameters that asymptotically follow a discrete double-exponential distribution. It is based on analysing generating functions Gh(z) whose dominant singularities converge to a certain value at an exponential rate. This behaviour is typically found by means of a bootstrapping approach. Our scheme is illustrated by a number of classical and new examples, such as the longest run in words or compositions, patterns in Dyck and Motzkin paths, or the maximum degree in planted plane trees.
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Submitted on : Thursday, September 10, 2015 - 3:17:35 PM
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Helmut Prodinger, Stephan Wagner. Bootstrapping and double-exponential limit laws. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2015, Vol. 17 no. 1 (1), pp.123--144. ⟨10.46298/dmtcs.2125⟩. ⟨hal-01196869⟩



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