Continuum tree limit for the range of random walks on regular trees
Continuum tree limit for the range of random walks on regular trees
Let b be an integer greater than 1 and let Wɛ=(Wɛn;n≥0) be a random walk on the b-ary rooted tree $\mathbb {U}_{b}$, starting at the root, going up (resp. down) with probability 1/2+ɛ (resp. 1/2−ɛ), ɛ∈(0,1/2), and choosing direction i∈{1,…,b} when going up with probability ai. Here a=(a1,…,ab) stands for …