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- W4385003389 abstract "We define a notion of multijet for functions on $mathbb{R}^n$, which extends the classical notion of jets in the sense that the multijet of a function is defined by contact conditions at several points. For all $p geq 1$ we build a vector bundle of $p$-multijets, defined over a well-chosen compactification of the configuration space of $p$ distinct points in $mathbb{R}^n$. As an application, we prove that the linear statistics associated with the zero set of a centered Gaussian field on a Riemannian manifold have a finite $p$-th moment as soon as the field is of class~$mathcal{C}^p$ and its $(p-1)$-jet is nowhere degenerate. We prove a similar result for the linear statistics associated with the critical points of a Gaussian field and those associated with the vanishing locus of a holomorphic Gaussian field." @default.
- W4385003389 created "2023-07-22" @default.
- W4385003389 creator A5067715129 @default.
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- W4385003389 date "2023-07-20" @default.
- W4385003389 modified "2023-10-17" @default.
- W4385003389 title "Multijet bundles and application to the finiteness of moments for zeros of Gaussian fields" @default.
- W4385003389 doi "https://doi.org/10.48550/arxiv.2307.10659" @default.
- W4385003389 hasPublicationYear "2023" @default.
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