There are many examples of physical phenomena that seem to be governed by non-Gaussian statistics. For instance the Levy distribution arises in the multiple scattering of light in turbid media, where the photon path length follows this distribution. I think any time you have rare but important events you will see non-gaussian statistics, such as with the distribution of sunspots, the time between geomagnetic reversals, etc. The Gaussian is nice since it leads to relatively easy analytic calculations (in addition to the reasons already given). In dynamical systems the level spacings of energy are governed (universally) by Poisson statistics for the case of nonchaotic systems, vs Wigner-type statistics for chaotic systems The whole field of Levy flights is huge. Especially in laser cooling. This book is superb: https://www.amazon.com/gp/search?index=books&linkCode=qs&keywords=9780521004220

There are many examples of physical phenomena that seem to be governed by non-Gaussian statistics. For instance, the Levy distribution arises in the multiple scattering of light in turbid media, where the photon path length follows this distribution.

I think any time you have rare, but important events, you will see non-Gaussian statistics, such as with the distribution of sunspots, the time between geomagnetic reversals, etc. The Gaussian is nice since it leads to relatively easy analytic calculations (in addition to the reasons already given). In dynamical systems the level spacings of energy are governed (universally) by Poisson statistics for the case of nonchaotic systems, vs. Wigner-type statistics for chaotic systems.

The whole field of Levy flights is huge. Especially in laser cooling. This book is superb: Lévy Statistics and Laser Cooling: How Rare Events Bring Atoms to Rest

There are many examples of physical phenomena that seem to be governed by non-Gaussian statistics. For instance the Levy distribution arises in the multiple scattering of light in turbid media, where the photon path length follows this distribution. I think any time you have rare but important events you will see non-gaussian statistics, such as with the distribution of sunspots, the time between geomagnetic reversals, etc. The Gaussian is nice since it leads to relatively easy analytic calculations (in addition to the reasons already given). In dynamical systems the level spacings of energy are governed (universally) by Poisson statistics for the case of nonchaotic systems, vs Wigner-type statistics for chaotic systems

There are many examples of physical phenomena that seem to be governed by non-Gaussian statistics. For instance the Levy distribution arises in the multiple scattering of light in turbid media, where the photon path length follows this distribution. I think any time you have rare but important events you will see non-gaussian statistics, such as with the distribution of sunspots, the time between geomagnetic reversals, etc. The Gaussian is nice since it leads to relatively easy analytic calculations (in addition to the reasons already given). In dynamical systems the level spacings of energy are governed (universally) by Poisson statistics for the case of nonchaotic systems, vs Wigner-type statistics for chaotic systems The whole field of Levy flights is huge. Especially in laser cooling. This book is superb: https://www.amazon.com/gp/search?index=books&linkCode=qs&keywords=9780521004220