Daecheol Kim

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math.PR2026

Inhomogeneous Long-Range First-Passage Percolation in a Random Vertex Environment

Shirshendu Chatterjee, Partha S. Dey, Daecheol Kim

We study inhomogeneous long-range first-passage percolation on $Z^{d}$ with edge passage times $∥ x - y ∥^{α} ω_{x y} / (V_{x} V_{y})$ , where vertex weights have polynomial uppe…

math.PR2026

Phase Transition and Fluctuation Results for First-Passage Percolation on Spread-Out Cycle Graphs

Partha S. Dey, Daecheol Kim

We study first-passage percolation on the $ℓ$ -spread-out one-dimensional cycle of size $n$ , where vertices are connected if their graph distance is at most $ℓ$ . We assign i.i…

math.PR2026

First-Passage Percolation on Spread-out line graphs: Microscopic Regime

Partha S. Dey, Daecheol Kim

We study first-passage percolation on the $ℓ$ -spread-out line graph, where each vertex $i \in {0, 1, \dots, n}$ is connected to all others at distance at most $ℓ$ . Here, we focu…