@article{6df6500c055c4293b8bb4047def31403,
title = "THE WIRED MINIMAL SPANNING FOREST ON THE POISSON-WEIGHTED INFINITE TREE",
abstract = "We study the spectral and diffusive properties of the wired minimal spanning forest (WMSF) on the Poisson-weighted infinite tree (PWIT). Let M be the tree containing the root in the WMSF on the PWIT and (Yn)n≥0 be a simple random walk on M starting from the root. We show that almost surely M has P[Y2n = Y0] = n-3/4+o(1) and dist(Y0, Yn) = n1/4+o(1) with high probability. That is, the spectral dimension of M is 3/2 and its typical displacement exponent is 1/4, almost surely. These confirm Addario–Berry{\textquoteright}s predictions (Addario-Berry (2013)).",
keywords = "Minimal spanning tree, Poisson-weighted infinite tree, local limit, spectral dimension, wired minimal spanning forest",
author = "Asaf Nachmias and Pengfei Tang",
note = "Publisher Copyright: {\textcopyright} Institute of Mathematical Statistics, 2024.",
year = "2024",
month = apr,
doi = "10.1214/23-AAP2027",
language = "אנגלית",
volume = "34",
pages = "2415--2446",
journal = "Annals of Applied Probability",
issn = "1050-5164",
publisher = "Institute of Mathematical Statistics",
number = "2",
}