In this short note we show that the paths two independent loop-erased random walks in four dimensions intersect infinitely often. We actually prove the stronger result that the cut-points of the two walks intersect infinitely often.
"Loop-Erased Walks Intersect Infinitely Often in Four Dimensions." Electron. Commun. Probab. 3 35 - 42, 1998. https://doi.org/10.1214/ECP.v3-991