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

dmtcs:2125 - Discrete Mathematics & Theoretical Computer Science, March 18, 2015, Vol. 17 no. 1
Bootstrapping and double-exponential limit laws

Authors: Prodinger, Helmut and Wagner, Stephan

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.


Source : oai:HAL:hal-01196869v1
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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