Bootstrapping and double-exponential limit laws
Helmut Prodinger, Stephan Wagner
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.
Full Text: PDF PostScript