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Peer-reviewedCC BY 4.0Electronic Notes in Discrete Mathematics

Lattice paths with catastrophes (short conference version)

  • Cyril Banderier
  • Michael Wallner
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Abstract

In queuing theory, it is usual to have some models with a reset of the queue. In terms of lattice paths, it is like having the possibility of jumping from any altitude to zero. These objects have the interesting feature that they do not have the same intuitive probabilistic behavior like classical Dyck paths (the typical properties of which are strongly related to Brownian motion theory), and this article quanties some relations between these two types of paths. We give a bijection with some other lattice paths and a link with a continuous fraction expansion, and prove several formulae for related combinatorial structures conjectured in the On-line Encyclopedia of Integer Sequences. Thanks to the kernel method and via analytic combinatorics, we derive the enumeration and limit laws of these lattice paths with catastrophes, for any nite set of jumps.

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Cite

BibTeXRIS
BibTeX
@article{banderier2026lattice,
  title = {{Lattice paths with catastrophes (short conference version)}},
  author = {Cyril Banderier and Michael Wallner},
  journal = {Electronic Notes in Discrete Mathematics},
  year = {2026},
  month = sep,
  doi = {10.1016/j.endm.2017.05.010},
  url = {https://hal.science/hal-05734821v1},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Lattice paths with catastrophes (short conference version)
AU  - Cyril Banderier
AU  - Michael Wallner
PY  - 2026
DA  - 2026/09/01
JO  - Electronic Notes in Discrete Mathematics
DO  - 10.1016/j.endm.2017.05.010
UR  - https://hal.science/hal-05734821v1
AB  - In queuing theory, it is usual to have some models with a reset of the queue. In terms of lattice paths, it is like having the possibility of jumping from any altitude to zero. These objects have the interesting feature that they do not have the same intuitive probabilistic behavior like classical Dyck paths (the typical properties of which are strongly related to Brownian motion theory), and this article quanties some relations between these two types of paths. We give a bijection with some other lattice paths and a link with a continuous fraction expansion, and prove several formulae for related combinatorial structures conjectured in the On-line Encyclopedia of Integer Sequences. Thanks to the kernel method and via analytic combinatorics, we derive the enumeration and limit laws of these lattice paths with catastrophes, for any nite set of jumps.
SN  - 1571-0653
ER  -