NODAL VOLUMES AS DIFFERENTIABLE FUNCTIONALS OF GAUSSIAN FIELDS

PECCATI, Giovanni; STECCONI, Michele

doi:10.1090/tran/9440

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NODAL VOLUMES AS DIFFERENTIABLE FUNCTIONALS OF GAUSSIAN FIELDS

PECCATI, Giovanni; STECCONI, Michele

2025 • In Transactions of the American Mathematical Society, 378 (9), p. 6585 - 6654

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10.1090/tran/9440

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Published electronically: May 1, 2025 Additional Notes: This research was supported by the Luxembourg National Research Fund (Grant: 021/16236290/HDSA)

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Keywords :

Mathematics (all); Applied Mathematics

Abstract :

[en] We characterize the absolute continuity of the law and the Malliavin-Sobolev regularity of random nodal volumes associated with smooth Gaussian fields on generic C2 manifolds with arbitrary dimension. Our results extend and generalize the seminal contribution by Angst and Poly (2020) about stationary fields on Euclidean spaces and cover, in particular, the case of two-dimensional manifolds, possibly with boundary and corners. The main tools exploited in the proofs include the use of Gaussian measures on Banach spaces, Morse theory, and the characterization of Malliavin-Sobolev spaces in terms of ray absolute continuity. Several examples are analyzed in detail.

Disciplines :

Mathematics

Author, co-author :

PECCATI, Giovanni ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)

STECCONI, Michele ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)

External co-authors :

Language :

English

Title :

NODAL VOLUMES AS DIFFERENTIABLE FUNCTIONALS OF GAUSSIAN FIELDS

Publication date :

September 2025

Journal title :

Transactions of the American Mathematical Society

ISSN :

0002-9947

eISSN :

1088-6850

Publisher :

American Mathematical Society

Volume :

378

Issue :

Pages :

6585 - 6654

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://www.ams.org/tran/0000-000-00/S0002-9947-2025-09440-6/tran9440_AM.pdf

Funders :

Fonds National de la Recherche Luxembourg
Fonds National de la Recherche Luxembourg

Funding text :

Received by the editors May 1, 2024, and, in revised form, November 4, 2024, and January 15, 2025. 2020 Mathematics Subject Classification. Primary 60G15, 60H07, 60G60, 58K05, 28A75. This research was supported by the Luxembourg National Research Fund (Grant: 021/16236290/HDSA).

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