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Ori Gurel-Gurevich
Ori Gurel-Gurevich
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Hello, How can one prove that the Lamplighter group on G=Z$G=\mathbb{Z}$ is Liouville. I have seen a stronger claim which states that the Lamplighter group over all recurrent graphs is Liouville. How can either of these claims be proved? Thank you very much!

Hello, How can one prove that the Lamplighter group on G=Z is Liouville. I have seen a stronger claim which states that the Lamplighter group over all recurrent graphs is Liouville. How can either of these claims be proved? Thank you very much!

Hello, How can one prove that the Lamplighter group on $G=\mathbb{Z}$ is Liouville. I have seen a stronger claim which states that the Lamplighter group over all recurrent graphs is Liouville. How can either of these claims be proved? Thank you very much!

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Daniel D
Daniel D
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Random walk and the liouville property

Hello, How can one prove that the Lamplighter group on G=Z is Liouville. I have seen a stronger claim which states that the Lamplighter group over all recurrent graphs is Liouville. How can either of these claims be proved? Thank you very much!