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DOI: 10.4230/LIPIcs.AofA.2022.15

Polyharmonic Functions in the Quarter Plane

Authors: Andreas Nessmann

Published in: LIPIcs, Volume 225, 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)

Abstract

In this article, a novel method to compute all discrete polyharmonic functions in the quarter plane for models with small steps, zero drift and a finite group is proposed. A similar method is then introduced for continuous polyharmonic functions, and convergence between the discrete and continuous cases is shown.

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Andreas Nessmann. Polyharmonic Functions in the Quarter Plane. In 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 225, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{nessmann:LIPIcs.AofA.2022.15,
  author =	{Nessmann, Andreas},
  title =	{{Polyharmonic Functions in the Quarter Plane}},
  booktitle =	{33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)},
  pages =	{15:1--15:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-230-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{225},
  editor =	{Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2022.15},
  URN =		{urn:nbn:de:0030-drops-161016},
  doi =		{10.4230/LIPIcs.AofA.2022.15},
  annote =	{Keywords: Polyharmonic functions, Functional equations, Lattice paths, Random walks, Brownian motion, Generating functions, Laplace transforms}
}

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