## Electronic Communications in Probability

- Electron. Commun. Probab.
- Volume 22 (2017), paper no. 12, 4 pp.

### The set of connective constants of Cayley graphs contains a Cantor space

#### Abstract

The connective constant of a transitive graph is the exponential growth rate of its number of self-avoiding walks. We prove that the set of connective constants of the so-called Cayley graphs contains a Cantor set. In particular, this set has the cardinality of the continuum.

#### Article information

**Source**

Electron. Commun. Probab., Volume 22 (2017), paper no. 12, 4 pp.

**Dates**

Received: 26 August 2016

Accepted: 13 January 2017

First available in Project Euclid: 27 January 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.ecp/1485507643

**Digital Object Identifier**

doi:10.1214/17-ECP43

**Mathematical Reviews number (MathSciNet)**

MR3607807

**Zentralblatt MATH identifier**

1357.82014

**Subjects**

Primary: 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]

**Keywords**

Cayley graph transitive graph connective constant uncountability

**Rights**

Creative Commons Attribution 4.0 International License.

#### Citation

Martineau, Sébastien. The set of connective constants of Cayley graphs contains a Cantor space. Electron. Commun. Probab. 22 (2017), paper no. 12, 4 pp. doi:10.1214/17-ECP43. https://projecteuclid.org/euclid.ecp/1485507643