Random walks in the quarter plane with zero drift: an explicit criterion for the finiteness of the associated group

Abstract : In many recent studies on random walks with small jumps in the quarter plane, it has been noticed that the so-called "group" of the walk governs the behavior of a number of quantities, in particular through its "order". In this paper, when the "drift" of the random walk is equal to 0, we provide an effective criterion giving the order of this group. More generally, we also show that in all cases where the "genus" of the algebraic curve defined by the kernel is 0, the group is infinite, except precisely for the zero drift case, where finiteness is quite possible.
Document type :
Journal articles
Complete list of metadatas

Cited literature [11 references]  Display  Hide  Download

https://hal.inria.fr/inria-00572276
Contributor : Guy Fayolle <>
Submitted on : Tuesday, March 1, 2011 - 10:55:50 AM
Last modification on : Friday, April 19, 2019 - 3:24:48 PM
Long-term archiving on : Monday, May 30, 2011 - 2:44:34 AM

Files

RR-7555.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : inria-00572276, version 1
  • ARXIV : 1103.0192

Collections

Citation

Guy Fayolle, Kilian Raschel. Random walks in the quarter plane with zero drift: an explicit criterion for the finiteness of the associated group. Markov Processes and Related Fields, Polymath, 2011, 17 (4), pp.619-636. ⟨inria-00572276⟩

Share

Metrics

Record views

368

Files downloads

396