First-Passage percolation on the square lattice / by Wierman, John C., Smythe, Robert T.

Batch queues, reversibility and first-passage percolation by Martin, J

“…As an application, we show how these results can be combined with methods of Seppalainen and O'Connell to provide exact solutions for a new class of first-passage percolation problems.…”

Comparison of limit shapes for Bernoulli first-passage percolation by Naoki Kubota, Masato Takei

Subjects: “…First-passage percolation…”
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Weak LQG metrics and Liouville first passage percolation by Dubédat, Julien, Falconet, Hugo, Gwynne, Ewain, Pfeffer, Joshua, Sun, Xin

“…(Tightness of Liouville first passage percolation for $$\gamma \in (0,2)$$γ∈(0,2), 2019. …”
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Topics in stochastic processes with special reference to first passage percolation theory by Welsh, JAD

“…<p>First passage percolation theory in its most general form is the randomised version of the well-known shortest route problem. …”

Stochastic Domination and Comb Percolation by Holroyd, A, Martin, J

“…This is proved using several new results and techniques involving stochastic domination, in contexts that include a process of independent overlapping intervals on Z, and first-passage percolation on general graphs.…”

A random hierarchical lattice: The series-parallel graph and its properties by Hambly, B, Jordan, J

“…We investigate the effective resistance across the graphs, first-passage percolation on the graphs and the Cheeger constants of the graphs as the number of edges tends to infinity. …”

A random hierarchical lattice: the series-parallel graph and its properties by Hambly, B, Jordan, J

“…We investigate the effective resistance across the graphs, first-passage percolation on the graphs and the Cheeger constants of the graphs as the number of edges tends to infinity. …”

Scaling Limits of Random Graphs from Subcritical Classes: Extended abstract by Konstantinos Panagiotou, Benedikt Stufler, Kerstin Weller

“…Our methods also enable us to study first passage percolation on $\mathsf{C}_n$, where we show the convergence to $\mathcal{T}_{\mathsf{e}}$ under an appropriate rescaling.…”
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Random geometry and the Kardar–Parisi–Zhang universality class by Silvia N Santalla, Javier Rodríguez-Laguna, Tom LaGatta, Rodolfo Cuerno

“…Results on related first-passage percolation problems lead us to postulate that the statistics of balls in these random metrics belong to the Kardar–Parisi–Zhang universality class of surface kinetic roughening, with ξ and χ relating to critical exponents characterizing a corresponding interface growth process. …”
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Renormalisation of random hierarchial systems by Jordan, J, Jordan, Jonathan

“…In one example, which is related to first-passage percolation on a random hierarchical lattice, we show the existence of a family of non-degenerate fixed points and show that the sequence of distributions will converge to one of these. …”