Geodesic
Random orders and gambler's ruin
The electronic journal of combinatorics, Tome 12 (2005)
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

We prove a conjecture of Droste and Kuske about the probability that $1$ is minimal in a certain random linear ordering of the set of natural numbers. We also prove generalizations, in two directions, of this conjecture: when we use a biased coin in the random process and when we begin the random process with a specified ordering of a finite initial segment of the natural numbers. Our proofs use a connection between the conjecture and a question about the game of gambler's ruin. We exhibit several different approaches (combinatorial, probabilistic, generating function) to the problem, of course ultimately producing equivalent results.
DOI : 10.37236/1920
Classification : 05A15, 05A19, 60C05
Mots-clés : random linear order 
@article{10_37236_1920,
     author = {Andreas Blass and G\'abor Braun},
     title = {Random orders and gambler's ruin},
     journal = {The electronic journal of combinatorics},
     year = {2005},
     volume = {12},
     doi = {10.37236/1920},
     zbl = {1075.05004},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1920/}
}
TY  - JOUR
AU  - Andreas Blass
AU  - Gábor Braun
TI  - Random orders and gambler's ruin
JO  - The electronic journal of combinatorics
PY  - 2005
VL  - 12
UR  - http://geodesic.mathdoc.fr/articles/10.37236/1920/
DO  - 10.37236/1920
ID  - 10_37236_1920
ER  - 
%0 Journal Article
%A Andreas Blass
%A Gábor Braun
%T Random orders and gambler's ruin
%J The electronic journal of combinatorics
%D 2005
%V 12
%U http://geodesic.mathdoc.fr/articles/10.37236/1920/
%R 10.37236/1920
%F 10_37236_1920
Andreas Blass; Gábor Braun. Random orders and gambler's ruin. The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1920

Cité par Sources :