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Session II.3 - Real-Number Complexity

Saturday, June 17, 16:30 ~ 17:00

On a general Kac-Rice formula for the measure of a level set

Diego Armentano

Universidad de la República, Uruguay   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Let $X(\cdot) $ be a random field from $\mathbb{R}^D$ to $\mathbb{R}^d$, $D\geq d$. In this talk we'll first study the level set $X^{-1}( u) $, $u \in \mathbb{R}^d$. In particular we'll give a weak condition for this level set to be rectifiable. Then, we will show how to establish a Kac-Rice formula to compute the $(D-d)$ Hausdorff measure. If time permits, we will conclude with some examples of application.

Joint work with José Rafael León (Universidad de la República, Uruguay) and Jean-Marc Azaïs (Université Paul Sabatier III, France).

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