most recent 30 from http://mathoverflow.net 2013-05-19T08:37:03Z http://mathoverflow.net/feeds/user/9625 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/40268/why-is-the-gaussian-so-pervasive-in-mathematics/40480#40480 Alex Bloemendal 2010-09-29T15:08:55Z 2010-09-29T15:08:55Z

<p>I'm not an expert, but I believe Stein's method gives a more satisfying connection between the CLT and the heat equation, in particular one that does not involve the Fourier transform. Stein's characterization of the normal distribution and convergence to normality involves an operator closely related to the generator of the Ornstein-Uhlenbeck process. On the other hand, the fact that latter has the Gaussian as its invariant measure can be obtained by a trivial transformation of the fundamental solution of the heat equation.</p>