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• 12:35, 14 January 2026 Lptmswikids talk contribs created page A Concrete Example: The Gaussian Case (Created page with "To understand how a universal scaling form emerges, let us analyze in detail the case of a Gaussian distribution with zero mean and variance <math>\sigma^2</math>. Using integration by parts, we can write : <center> <math>P^<(E) = \int_{-\infty}^E \frac{dx}{\sqrt{2 \pi \sigma^2}} \, e^{-\frac{x^2}{2 \sigma^2}} = \frac{1}{2\sqrt{\pi}} \int_{\frac{E^2}{2 \sigma^2}}^{\infty} \frac{dt}{\sqrt{t}} e^{-t}= \frac{\sigma}{\sqrt{2 \pi} |E|} e^{-\frac{E^2}{2 \sigma^2}} - \frac{1}{4...")