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  "body": "\n## Summary\n\nThe Martin kernel of a domain is the [[Green's function|M36SD56MWQ]] normalised by its value at a fixed reference point: $M(x, y) = G(x, y) / G(x_0, y)$.\nAs the pole $y$ runs to the boundary, the functions $M(\\cdot, y)$ accumulate at positive harmonic functions.\nThese limits are the points of the Martin boundary.\nFor a ball, the limits are the Poisson kernels, so the Martin kernel generalises the [[Poisson kernel|TCYSWCTYYM]] to arbitrary domains.\n\n## Explanations\n\n### L1 human\n\nPut a unit charge at a point $y$ of a grounded domain and measure the potential at $x$.\nDivide by the potential at a fixed point $x_0$, so that the value at $x_0$ is always $1$.\nThis ratio is the Martin kernel.\nWhen $y$ approaches the boundary the potential itself tends to zero, but the ratio usually tends to a nonzero positive harmonic function.\nFor the unit ball these limits are the Poisson kernels, which describe how boundary values spread inside.\n",
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