Minghao Pan

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math.PR2026

Return Probability for the Switch--Walk--Switch Lamplighter Walk on a Regular Tree

Chenyang An, Minghao Pan

We derive the sharp return-probability asymptotic for the switch--walk--switch lamplighter walk with lamp group $Z_{2}$ over the infinite $d$ -regular tree: \[ p_{2n}(e,e) = ρ…

math.PR2024

Dimension jump at the uniqueness threshold for percolation in $\infty + d$ dimensions

Tom Hutchcroft, Minghao Pan

Consider percolation on $T \times Z^{d}$ , the product of a regular tree of degree $k \geq 3$ with the hypercubic lattice $Z^{d}$ . It is known that this graph has $0<p_c…

math.PR2024

Percolation at the uniqueness threshold via subgroup relativization

Tom Hutchcroft, Minghao Pan

We study percolation on nonamenable groups at the uniqueness threshold $p_{u}$ , the critical value that separates the phase in which there are infinitely many infinite clusters from…

Return Probability for the Switch--Walk--Switch Lamplighter Walk on a Regular Tree

Dimension jump at the uniqueness threshold for percolation in ∞+d dimensions

Percolation at the uniqueness threshold via subgroup relativization

Dimension jump at the uniqueness threshold for percolation in $\infty + d$ dimensions