Critical intensity conjecture for the Manhattan grid model
Critical intensity conjecture for the Manhattan grid model
Let denote the critical intensity in the phase transition theorem for , and consider the Boolean model generated by a homogeneous Poisson point process in two dimensions. Critical intensity conjecture. The quantity is the critical intensity for the Boolean model of a homogeneous Poisson point process in two dimensions.
The conjecture identifies the critical intensity of the Manhattan grid model's limiting high-street-intensity regime with the corresponding planar Boolean-model threshold. The supplied text gives no resolution, so the claim remains open.
Sources & referencesView supporting material
Primary source
Benedikt Jahnel, Sanjoy Kumar Jhawar and Anh Duc Vu, “Continuum Percolation in a Nonstabilizing Environment”, arXiv:2205.15366 (2023).
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