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⟨x2⟩=2Dt\langle x^{2} \rangle = 2Dt

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the diffusion equation, in a form still written the same way today [ 1 ] . Solving it for particles released from a point gives a spreading distribution whose variance grows linearly, not with the square root of time as a naive guess might suggest but as ⟨x2⟩=2Dt\langle x^{2} \rangle = 2Dt. with the diffusion constant D fixed by measurable quantities. Einstein derived it explicitly, from the balance between the drag on a sphere of radius P in a fluid of viscosity k and the osmotic pressure driving diffusion, as

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⟨x2⟩=2Dt,\langle x^{2} \rangle = 2Dt,

Equation 3 · Einstein & Evolution

Einstein's Random Walk and the Mathematics of Genetic Drift

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

the diffusion equation, in a form still written the same way today [ 1 ] . Solving it for particles released from a point gives a spreading distribution whose variance grows linearly, not with the square root of time as a naive guess might suggest but as ⟨x2⟩=2Dt\langle x^{2} \rangle = 2Dt. with the diffusion constant D fixed by measurable quantities. Einstein derived it explicitly, from the balance between the drag on a sphere of radius P in a fluid of viscosity k and the osmotic pressure driving diffusion, as

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