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Random rotational invariance of integration by parts formulas within a Bismut-type approach
Susanna Deh\`o, Francesco C. De Vecchi, Paola Morando, Stefania Ugolini
https://arxiv.org/abs/2506.11937

Random rotational invariance of integration by parts formulas within a Bismut-type approach
The stochastic rotational invariance of an integration by parts formula inspired by the Bismut approach to Malliavin calculus is proved in the framework of the Lie symmetry theory of stochastic differential equations. The non-trivial effect of the rotational invariance of the driving Brownian motion in the derivation of the integration by parts formula is discussed and the invariance property of the formula is shown via applications to some explicit two-dimensional Brownian motion-driven stocha…

Compact representation and long-time extrapolation of real-time data for quantum systems
Andre Erpenbeck, Yuanran Zhu, Yang Yu, Lei Zhang, Richard Gerum, Olga Goulko, Chao Yang, Guy Cohen, Emanuel Gull
https://arxiv.org/abs/2506.13760

Compact representation and long-time extrapolation of real-time data for quantum systems
Representing real-time data as a sum of complex exponentials provides a compact form that enables both denoising and extrapolation. As a fully data-driven method, the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm is agnostic to the underlying physical equations, making it broadly applicable to various observables and experimental or numerical setups. In this work, we consider applications of the ESPRIT algorithm primarily to extend real-time dynamical d…

This https://arxiv.org/abs/2310.19611 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Exchangeability and irreducible rotational invariance
In this note we prove that a finite family $\{X_1,\dots,X_d\}$ of real r.v.'s that is exchangeable and such that $(X_1,\dots,X_d)$ is invariant with respect to a subgroup of $SO(d)$ acting irreducibly, is actually invariant with respect to the action of the full group $SO(d)$. Three immediate consequences are deduced: a characterization of isotropic spherical random eigenfunctions whose Fourier coefficients are exchangeable, an extension of Bernstein's characterization of the Gaussian and a cha…