Multijet bundles and application to the finiteness of moments for zeros of Gaussian fields

Ancona, Michele; Letendre, Thomas

doi:10.2140/apde.2025.18.1433

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1948-206X (online)

ISSN 2157-5045 (print)

Author index

To appear

Other MSP journals

Multijet bundles and application to the finiteness of moments for zeros of Gaussian fields

Michele Ancona and Thomas Letendre

Vol. 18 (2025), No. 6, 1433–1476

DOI: 10.2140/apde.2025.18.1433

Abstract

We define a notion of multijet for functions on $ℝ^{n}$ , 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 $ℝ^{n}$ . 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 $𝒞^{p}$ 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.

Keywords

compactification of configuration spaces, Gaussian fields, moments, multijets, random submanifolds

Mathematical Subject Classification

Primary: 51M15, 51M25, 55R80, 58A20, 60D05, 60G60

Milestones

Received: 1 October 2023

Accepted: 24 May 2024

Published: 29 May 2025

Authors

Michele Ancona
Université Côte d’Azur CNRS, LJAD Nice France

Thomas Letendre
Université Paris-Saclay CNRS, LMO Orsay France

Open Access made possible by participating institutions via Subscribe to Open.

Vol. 18, No. 6, 2025