The Boosted Loop-Erased Random Walk

2023.12.22 16:00 N613 

We introduce a novel near-critical version of the loop-erased random walk (LERW) by boosting the weight of random walk path according to its length before loop-erasure. We construct the scaling limit in natural parametrization in two and three dimensions and show that the boosted scaling limit undergoes a phase transition and that the boosted scaling limit gradually becomes space-filling as the perturbation parameter tends to infinity. In particular, these results provide some evidence to a conjecture of Makarov-Smirnov on 2D near-critical lattice models. Based on joint works (in progress) with Gefei Cai, Aoteng Xia (Peking), Sarai Hernandez-Torres (UNAM) and Daisuke Shiraishi (Kyoto).