Geodesic
A sharp threshold for collapse of the random triangular group
Sylwia Antoniuk1 ; Ehud Friedgut2 ; Tomasz Łuczak1
1Adam Mickiewicz University, Poznán, Poland
2Weizmann Institute of Science, Rehovot, Israel
Groups, geometry, and dynamics, Tome 11 (2017) no. 3, pp. 879-890

Voir la notice de l'article provenant de la source EMS Press

DOI

The random triangular group Γ(n,p) is the group given by a random group presentation with n generators in which every relator of length three is present independently with probability p. We show that in the evolution of €Γ(n,p) the property of collapsing to the trivial group admits a very sharp threshold.
DOI : 10.4171/ggd/417
Classification : 20-XX, 05-XX
Mots-clés : Random group, collapse, sharp threshold, torsion-free

Sylwia Antoniuk  1   ; Ehud Friedgut  2   ; Tomasz Łuczak  1

1 Adam Mickiewicz University, Poznán, Poland
2 Weizmann Institute of Science, Rehovot, Israel 
Sylwia Antoniuk; Ehud Friedgut; Tomasz Łuczak. A sharp threshold for collapse of the random triangular group. Groups, geometry, and dynamics, Tome 11 (2017) no. 3, pp. 879-890. doi: 10.4171/ggd/417
@article{10_4171_ggd_417,
     author = {Sylwia Antoniuk and Ehud Friedgut and Tomasz {\L}uczak},
     title = {A sharp threshold for collapse of the random triangular group},
     journal = {Groups, geometry, and dynamics},
     pages = {879--890},
     year = {2017},
     volume = {11},
     number = {3},
     doi = {10.4171/ggd/417},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/417/}
}
TY  - JOUR
AU  - Sylwia Antoniuk
AU  - Ehud Friedgut
AU  - Tomasz Łuczak
TI  - A sharp threshold for collapse of the random triangular group
JO  - Groups, geometry, and dynamics
PY  - 2017
SP  - 879
EP  - 890
VL  - 11
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ggd/417/
DO  - 10.4171/ggd/417
ID  - 10_4171_ggd_417
ER  - 
%0 Journal Article
%A Sylwia Antoniuk
%A Ehud Friedgut
%A Tomasz Łuczak
%T A sharp threshold for collapse of the random triangular group
%J Groups, geometry, and dynamics
%D 2017
%P 879-890
%V 11
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/417/
%R 10.4171/ggd/417
%F 10_4171_ggd_417

Cité par Sources :