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# Polyharmonic Functions in the Quarter Plane

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LIPIcs.AofA.2022.15.pdf
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## Acknowledgements

I would like to thank Kilian Raschel for introducing me to this topic as well as for a lot of valuable input and many fruitful discussions. Also, I would like to thank the anonymous reviewers for their valuable remarks.

## Cite As

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)
https://doi.org/10.4230/LIPIcs.AofA.2022.15

## 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.

## Subject Classification

##### ACM Subject Classification
• Theory of computation → Random walks and Markov chains
• Mathematics of computing → Markov processes
• Mathematics of computing → Generating functions
• Mathematics of computing → Combinatorics
##### Keywords
• Polyharmonic functions
• Functional equations
• Lattice paths
• Random walks
• Brownian motion
• Generating functions
• Laplace transforms

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