Geodesic
Lattice paths with catastrophes
Discrete mathematics & theoretical computer science, Tome 19 (2017-2018) no. 1.

Voir la notice de l'article provenant de la source Episciences

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 behaviour as classical Dyck paths (the typical properties of which are strongly related to Brownian motion theory), and this article quantifies some relations between these two types of paths. We give a bijection with some other lattice paths and a link with a continued fraction expansion. Furthermore, we 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 provide the enumeration and limit laws of these "lattice paths with catastrophes" for any finite set of jumps. We end with an algorithm to generate such lattice paths uniformly at random. 
@article{DMTCS_2017_19_1_a24,
     author = {Banderier, Cyril and Wallner, Michael},
     title = {Lattice paths with catastrophes},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2017-2018},
     doi = {10.23638/DMTCS-19-1-23},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-1-23/}
}
TY  - JOUR
AU  - Banderier, Cyril
AU  - Wallner, Michael
TI  - Lattice paths with catastrophes
JO  - Discrete mathematics & theoretical computer science
PY  - 2017-2018
VL  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-1-23/
DO  - 10.23638/DMTCS-19-1-23
LA  - en
ID  - DMTCS_2017_19_1_a24
ER  - 
%0 Journal Article
%A Banderier, Cyril
%A Wallner, Michael
%T Lattice paths with catastrophes
%J Discrete mathematics & theoretical computer science
%D 2017-2018
%V 19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-1-23/
%R 10.23638/DMTCS-19-1-23
%G en
%F DMTCS_2017_19_1_a24
Banderier, Cyril; Wallner, Michael. Lattice paths with catastrophes. Discrete mathematics & theoretical computer science, Tome 19 (2017-2018) no. 1. doi : 10.23638/DMTCS-19-1-23. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-1-23/

Cité par Sources :