Browsing Department of Pure Mathematics and Mathematical Statistics (DPMMS) by Subject "harmonic function"
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A Liouville hyperbolic souvlaki
(Institute of Mathematical StatisticsElectronic Journal of Probability, 20170425)We construct a transient boundeddegree graph no transient subgraph of which embeds in any surface of finite genus. Moreover, we construct a transient, Liouville, boundeddegree, Gromov–hyperbolic graph with trivial ...

Connective constants and height functions for Cayley graphs
(American Mathematical SocietyTransactions of the American Mathematical Society, 20170331)The connective constant $μ$($G$) of an infinite transitive graph $G$ is the exponential growth rate of the number of selfavoiding walks from a given origin. In earlier work of Grimmett and Li, a locality theorem was proved ...