Year: 2026
Type: preprint
Abstract: We study inhomogeneous long-range first-passage percolation on $\mathbb{Z}^d$ with edge passage times $\lVert x-y\rVert^αω_{xy}/(V_xV_y)$, where vertex weights have polynomial upper-tail exponent $γ$ and edge noises have polynomial lower-tail exponent $θ$ at zero. The model interpolates between long-range first-passage percolation and scale-free percolation and exhibits competition between reusable heavy-vertex hubs and pair-specific small-noise bridges. We conjecture an eight-regime phase diagram, organized into five growth phases governed by $q_{\rm hub}=d/γ$ and $q_{\rm edge}=d/θ$. For $T_n=T(0,\lceil nx\rceil)$, we prove upper bounds of the conjectured order in every regime and matching lower bounds in phases I and II. Specifically, $T_n=0$ a.s. when $α
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213610149