S. Mellick

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math.GR2023

Gaboriau's criterion and fixed price one for locally compact groups

Sam Mellick

Let $G_{1}$ be a semisimple real Lie group and $G_{2}$ another locally compact second countable unimodular group. We prove that $G_{1} \times G_{2}$ has fixed price one if $G_{1}$ has higher…

math.GR2021

The Palm groupoid of a point process and factor graphs on amenable and Property (T) groups

Sam Mellick

We define a probability measure preserving and r-discrete groupoid that is associated to every invariant point process on a locally compact and second countable group. This groupoi…