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math.PR2026
Range convergence and sharp one-arm asymptotics for the critical percolation cluster in high dimensions
M. Cabezas, D. Croydon, A. Fribergh +1
For critical Bernoulli bond percolation on in the high-dimensional regime, we prove that the rescaled empirical measure of the cluster of the origin converges, in a suitable…
math.PR2026
Collision properties of the four-dimensional random walk trace
David A. Croydon, Daisuke Shiraishi, Satomi Watanabe
We consider collisions of multiple random walks on the trace of a simple random walk on the four-dimensional integer lattice. For two independent walks (in continuous time), we app…