Electronic Communications in Probability

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

Sébastien Martineau

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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

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

Received: 26 August 2016
Accepted: 13 January 2017
First available in Project Euclid: 27 January 2017

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Zentralblatt MATH identifier

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

Cayley graph transitive graph connective constant uncountability

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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

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