Equation 31 · Einstein's Random Walk and the Mathematics of Genetic Drift
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Symbol p
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What the article says around this equation
A loose analogy would have stopped at the word “random”: both processes involve chance, so both get called a random walk, and the resemblance ends where the metaphor stops being convenient. A formal analogy goes further and insists on the correspondence term by term — a state variable, a drift coefficient, a diffusion coefficient, a pair of boundary conditions — and demands that solving one equation solve both problems at once, which is exactly what happened when Kimura’s boundary conditions turned out to be Einstein’s diffusion equation with absorbing walls added. That is what a formal analogy done right looks like, and it is the reason a page of Kimura’s diffusion equation and a page of…
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A loose analogy would have stopped at the word “random”: both processes involve chance, so both get called a random walk, and the resemblance ends where the metaphor stops being convenient. A formal analogy goes further and insists on the correspondence term by term — a state variable, a drift coefficient, a diffusion coefficient, a pair of boundary conditions — and demands that solving one equation solve both problems at once, which is exactly what happened when Kimura’s boundary conditions turned out to be Einstein’s diffusion equation with absorbing walls added. That is what a formal analogy done right looks like, and it is the reason a page of Kimura’s diffusion equation and a page of Einstein’s, with the axis labels covered, are the same page with x renamed p .
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