Analysis of Bidirectional Ballot Sequences and Random Walks Ending in Their Maximum

  title={Analysis of Bidirectional Ballot Sequences and Random Walks Ending in Their Maximum},
  author={Benjamin Hackl and Clemens Heuberger and H. Prodinger and Stephan G. Wagner},
  journal={Annals of Combinatorics},
Consider non-negative lattice paths ending at their maximum height, which will be called admissible paths. We show that the probability for a lattice path to be admissible is related to the Chebyshev polynomials of the first or second kind, depending on whether the lattice path is defined with a reflective barrier or not. Parameters like the number of admissible paths with given length or the expected height are analyzed asymptotically. Additionally, we use a bijection between admissible random… 
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