On the nature of the generating series of walks in the quarter plane

In the present paper, we introduce a new approach, relying on the Galois theory of difference equations, to study the nature of the generating series of walks in the quarter plane. Using this approach, we are not only able to recover many of the recent results about these series, but also to go beyo...

Full description

Saved in:
Bibliographic Details
Published in:Inventiones mathematicae 2018-07, Vol.213 (1), p.139-203
Main Authors: Dreyfus, Thomas, Hardouin, Charlotte, Roques, Julien, Singer, Michael F.
Format: Article
Language:English
Subjects:
Difference equations
Differential equations
General Mathematics
Mathematics
Mathematics and Statistics
Rational functions
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In the present paper, we introduce a new approach, relying on the Galois theory of difference equations, to study the nature of the generating series of walks in the quarter plane. Using this approach, we are not only able to recover many of the recent results about these series, but also to go beyond them. For instance, we give for the first time hypertranscendency results, i.e., we prove that certain of these generating series do not satisfy any nontrivial nonlinear algebraic differential equation with rational function coefficients.
ISSN:0020-9910
1432-1297
DOI:10.1007/s00222-018-0787-z