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  "body": "\n## Summary\n\nStochastic geometry is the part of probability theory that studies random geometric structures in space.\nIts main objects are [[point processes|DNDKBVHS3H]], random closed sets, random tessellations and random measures.\nTypical models are the [[Poisson point process|0MTNR28K60]] and the [[Boolean model|NK3CZTVEJD]].\nIt supplies models and formulas for random patterns in materials science, wireless networks, biology and image analysis.\n\n## Explanations\n\n### L1 human\n\nStochastic geometry asks questions about shapes that are placed at random.\nThink of raindrops on a pavement, trees in a forest, or cells seen under a microscope.\nOne models the centres as random points and the objects as random shapes around them.\nFor example, drop discs of radius $r$ at the points of a Poisson process of intensity $\\lambda$ in the plane.\nThen the fraction of the plane covered by the discs is $1 - e^{-\\lambda \\pi r^2}$.\nClassical questions of geometric probability, such as [[Buffon's needle problem|06X5PF6YFP]], belong to the same circle of ideas.\n",
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