Sample post with formulas

A sample post, safe to delete. It carries math: true in its header, which is what loads MathJax; posts without formulas skip the script. The semicircle law has density $\frac{1}{2\pi}\sqrt{4-x^2}$ on $[-2,2]$, and it plays the role in free probability that the Gaussian plays in the classical theory.

Inline formulas go between single dollar signs, displayed ones between double dollar signs on their own lines. Free convolution is linearized by the $R$-transform:

\[R_{\mu \boxplus \nu}(z) = R_\mu(z) + R_\nu(z),\]

and for the semicircle law of variance $t$ one has $R(z) = tz$, so semicircle laws form a semigroup under $\boxplus$, just as Gaussians do under ordinary convolution.

One thing to know. Markdown reads the text before MathJax does, and it occasionally takes a pair of * or _ inside single dollars for emphasis: $a^*b^*$ is the classic victim. If a formula comes out mangled, write it with double dollars inline, like this: \(a^*b^*\). Markdown leaves everything between double dollars alone, and in the middle of a sentence it still comes out as an inline formula.