Maarten Markering

collaborators

3 papers

math.PR2026

The scaling limit of random walk and the intrinsic metric on planar critical percolation

Irina Đanković, Maarten Markering, Jason Miller +1

We consider critical site percolation ( $p = p_{c} = 1/2$ ) on the triangular lattice $T$ in two dimensions. We show that the simple random walk on the clusters of open vertices c…

math.PR2024

Capacity of loop-erased random walk

Maarten Markering

We study the capacity of loop-erased random walk (LERW) on $Z^{d}$ . For $d \geq 4$ , we prove a strong law of large numbers and give explicit expressions for the limit in terms…

math.PR2024

Two-sided infinite self-avoiding walk in high dimensions

Maarten Markering

We construct the two-sided infinite self-avoiding walk (SAW) on $Z^{d}$ for $d \geq 5$ and use it to prove pattern theorems for the self-avoiding walk. We show that infinite t…