A sharp threshold for collapse of the random triangular group

Sylwia Antoniuk; Ehud Friedgut; Tomasz Łuczak

doi:10.4171/GGD/417

A sharp threshold for collapse of the random triangular group

Sylwia Antoniuk, Ehud Friedgut, Tomasz Łuczak

Department of Mathematics

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	879-890
Number of pages	12
Journal	Groups Geometry And Dynamics
Volume	11
Issue number	3
DOIs	https://doi.org/10.4171/GGD/417
State	Published - 2017

All Science Journal Classification (ASJC) codes

Geometry and Topology
Discrete Mathematics and Combinatorics

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10.4171/GGD/417

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title = "A sharp threshold for collapse of the random triangular group",

abstract = "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.",

author = "Sylwia Antoniuk and Ehud Friedgut and Tomasz {\L}uczak",

note = "Publisher Copyright: {\textcopyright} European Mathematical Society.",

year = "2017",

doi = "10.4171/GGD/417",

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AU - Antoniuk, Sylwia

AU - Friedgut, Ehud

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N2 - 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.

AB - 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.

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U2 - 10.4171/GGD/417

DO - 10.4171/GGD/417

M3 - مقالة

SN - 1661-7207

VL - 11

SP - 879

EP - 890

JO - Groups Geometry And Dynamics

JF - Groups Geometry And Dynamics

IS - 3

ER -

A sharp threshold for collapse of the random triangular group

Abstract

All Science Journal Classification (ASJC) codes

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