Gaussian behavior on hyperplanes

Daniel Fresen

Published 2011-08-25, updated 2015-09-13Version 3

We observe that the function $\Lambda _{n}:\mathbb{R}^{n}\rightarrow (0,\infty )$ defined by \begin{equation*} \Lambda _{n}(x)=\exp \left( x_{1}-\pi \sum_{i=2}^{n}x_{i}^{2}\right) \end{equation*} appears in the tails of a large class of functions, with properties involving log-concavity, independence, and homogeneity, as well as the gamma function.