Critical intensity conjecture for the Manhattan grid model

Let Ic>0I_c>0 denote the critical intensity in the phase transition theorem for I=(μ+μ)λI=(\mu+\mu)\cdot\lambda, and consider the Boolean model generated by a homogeneous Poisson point process in two dimensions. Critical intensity conjecture. The quantity IcI_c 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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