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math.PR2024
A unimodular random graph with large upper growth and no growth
Péter Mester, Ádám Timár
We construct a unimodular random rooted graph with maximal degree and upper growth rate , which does not have a growth rate. Abért, Fraczyk and Hayes showed that for…
math.PR2024
Invariant splitting of a slab into infinitely many robust clusters
Péter Mester
We give an example of an invariant bond percolation process on the slab with the property that it has infinitely many clusters whose critical percolati…