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Daecheol Kim

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Preprint Sep 2026

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

We study inhomogeneous long-range first-passage percolation on $\mathbb{Z}^d$ with edge passage times $\lVert x-y\rVert^\alpha\omega_{xy}/(V_xV_y)$, where vertex weights have polynomial upper-tail exponent $\gamma$ and edge noises have polynomial lower-tail exponent $\theta$ at zero. The model interpolates between long...

Shirshendu Chatterjee, P. Dey, Daecheol Kim · 0 citations
Preprint Jul 2026

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

We study first-passage percolation on the $\ell$-spread-out line graph, where each vertex $i\in\{0,1,\dots,n\}$ is connected to all others at distance at most $\ell$. Here, we focus on the microscopic regime, with $\ell$ fixed as $n\to\infty$. Independent nonnegative weights are assigned to these edges. We obtain a law...

P. Dey, Daecheol Kim · 1 citation
Preprint Aug 2026

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

We study first-passage percolation on the $\ell$-spread-out one-dimensional cycle of size $n$, where vertices are connected if their graph distance is at most $\ell$. We assign i.i.d.~non-negative random weights from a Weibull distribution $\omega_e \sim \mathrm{Exp}(1)^{1/\theta}$ to the edges for $\theta>0$ fixed. Th...

P. Dey, Daecheol Kim · 1 citation

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