Helmut Prodinger ; Stephan Wagner - Bootstrapping and double-exponential limit laws

dmtcs:2125 - Discrete Mathematics & Theoretical Computer Science, March 18, 2015, Vol. 17 no. 1 - https://doi.org/10.46298/dmtcs.2125
Bootstrapping and double-exponential limit lawsArticle

Authors: Helmut Prodinger 1; Stephan Wagner 1

  • 1 Department of Mathematical Sciences [Matieland, Stellenbosch Uni.]

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.

Volume: Vol. 17 no. 1
Section: Combinatorics
Published on: March 18, 2015
Submitted on: May 15, 2012
Keywords: asymptotic scheme,bootstrapping,generating functions,double-exponential distribution,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC]

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