Asymptotic behavior of the heat equation in free space

I always appreciate self-contained efforts to summarize thinking on basic topics. In contrast to textbooks, which by necessity need to address a broad set of techniques, a deep dive on one familiar topic can reveal the strengths and weaknesses of various mathematical perspectives.

To that end, I enjoyed this note by Juan Luis Vázquez on the heat equation.

“Asymptotic behaviour methods for the Heat Equation. Convergence to the Gaussian.” (arxiv 1706.10034)

As usual, a paper like this is “not publishable” and so does not appear in an official journal. And yet, because it is so useful, it has already been cited 21 times.