Différences
Ci-dessous, les différences entre deux révisions de la page.
| Les deux révisions précédentes Révision précédente | Prochaine révisionLes deux révisions suivantes | ||
| mega:seminaire [2024/03/23 17:07] – [Prochaine séance] Guillaume BARRAQUAND | mega:seminaire [2024/03/23 17:08] – [Prochaine séance] Guillaume BARRAQUAND | ||
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| Ligne 24: | Ligne 24: | ||
| Abstract: | Abstract: | ||
| - | * 14h00-15h00: | + | * 14h00-15h00: |
| Abstract: Let $X = \{ X(t),t \in \mathbb R^N\}$ be a centered Gaussian random field with values in $\mathbb R^d$ satisfying certain conditions and let $F \subset \mathbb R^d$ be a Borel set. In the talk, we provide a sufficient condition for $F$ to be polar for $X$, i.e. $P(X(t) \in F$ for some $t \in \mathbb R^N$) = 0, which improves significantly the existence results. We provide a variety of examples of Gaussian random field for which our result is applicable. Moreover, we solve a problem on the existence of collisions of the eigenvalues of random matrices with Gaussian random field entries that was left open in literature. | Abstract: Let $X = \{ X(t),t \in \mathbb R^N\}$ be a centered Gaussian random field with values in $\mathbb R^d$ satisfying certain conditions and let $F \subset \mathbb R^d$ be a Borel set. In the talk, we provide a sufficient condition for $F$ to be polar for $X$, i.e. $P(X(t) \in F$ for some $t \in \mathbb R^N$) = 0, which improves significantly the existence results. We provide a variety of examples of Gaussian random field for which our result is applicable. Moreover, we solve a problem on the existence of collisions of the eigenvalues of random matrices with Gaussian random field entries that was left open in literature. | ||