I am reading this paper. In section 1.1 he says:
What do the tildes above the letters mean? How can I translate these two sentences into ordinary English?
2026-04-06 16:51:55.1775494315
In probability notation: what does a tilde over a letter mean?
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The tilde can have a variety of meanings in different contexts, but as is made clear later in the paper, the tilde over the $p$ is being used there to indicate an empirical probability function (rather than a theoretical model/population probability function) - that is, one made from the sample proportions of each of the symbols.
That's consistent with the definition in the section you refer to.