Great answer, thank's a lot.
I didn't know I had to specify what other departments I'm applying to (I haven't checked the application forms in detail yet). I thought I could get away with it unnoticed hehe. Indeed, I probably will send some double applications to, say, Statistics (broadly speaking, my interests lie within probability and ergodic theory, but my interests are limited by the limited amount of time I had to read math, I would also like to learn more about dynamics in homogeneous spaces, for instance). I guess it is similar to the case of having an interest in logic, model theory or computability theory. The double application to CS makes sense there since there is an overlap of interests. However, an application to an Economics department can't be interpreted that way, they'll probably infer (somewhat correctly) that my interests are not limited to maths, and that my interest in doing math has no lexicographic priority over other variables such as prestige.
Thanks again for your answer!