arXiv subjects

Filippo Giovagnini

Publications and source records attributed to Filippo Giovagnini.

5 recordsLinked to original sources

arXiv2026

From Information to Delegation: Mapping Human-AI Financial Decision Making

As AI increasingly participates in human decision making, understanding how decision-making authority is distributed between humans and AI has become a fundamental behavioural question. We introduce a behavioural measurement framework combining intent and delegated decision authority to quantify what consumers seek from AI and how much decision-making authority they assign to it. Applied to 1.5 million real-world ChatGPT and Gemini interactions from 6,304 users in the United States and India, we find that financial services are already a substantial AI use case. Consumers overwhelmingly use AI to retrieve information and shape financial judgement, while delegation of financial execution remains rare. By shifting attention from conversation topics to delegated decision authority, this work establishes a behavioural baseline for measuring the transition to increasingly agentic AI.

cs.HC↗

arXiv2026

Non-selection of Lagrangian trajectories in the zero-noise limit for a class of stochastic regularizations

We prove the lack of selection in the zero-noise limit for solutions to SDEs driven by a divergence-free, H\"older continuous vector field with exponent $\alpha\in(0,1)$, arbitrarily close to $1$ but fixed. The result applies to a broad class of regularizing additive noises, including fractional Brownian motion and stable L\'evy processes. The proof combines pathwise Lagrangian arguments, based on the analysis of the deterministic flows associated to mixing velocity fields, with probabilistic estimates coming from the stochastic sewing lemma. This allows to show that lack of selection happens simultaneously on a large set of initial data, whose complement has arbitrarily small Lebesgue measure.

math.PR↗

arXiv2026

Universality in Deep Neural Networks: An approach via the Lindeberg exchange principle

We consider the infinite-width limit of a fully connected deep neural network with general weights, and we prove quantitative general bounds on the $2$-Wasserstein distance between the network and its infinite-width Gaussian limit, under appropriate regularity assumptions on the activation function. Our main tool is a Lindeberg principle for Deep Neural Networks, which we use to successively replace the weights on each layer by Gaussian random variables.

math.PR↗

arXiv2025

A uniform point vortex approximation for the solution of the two-dimensional Navier Stokes equation with transport noise

We study a model of interacting particles represented by a system of N stochastic differential equations. We establish that the mollified empirical distribution of the system converges uniformly with respect to both time and spatial variables to the solution of the two dimensional Navier Stokes equation with transport noise. The proofs are based on a semigroup approach.

math.PR↗

arXiv2025

A uniform particle approximation to the Navier-Stokes-alpha models in three dimensions with advection noise

In this work, we investigate a system of interacting particles governed by a set of stochastic differential equations. Our main goal is to rigorously demonstrate that the empirical measure associated with the particle system converges uniformly, both in time and space, to the solution of the three dimensional Navier Stokes alpha model with advection noise. This convergence establishes a probabilistic framework for deriving macroscopic stochastic fluid equations from underlying microscopic dynamics. The analysis leverages semigroup techniques to address the nonlinear structure of the limiting equations, and we provide a detailed treatment of the well posedness of the limiting stochastic partial differential equation. This ensures that the particle approximation remains stable and controlled over time. Although similar convergence results have been obtained in two dimensional settings, our study presents the first proof of strong uniform convergence in three dimensions for a stochastic fluid model derived from an interacting particle system. Importantly, our results also yield new insights in the deterministic regime, namely, in the absence of advection noise, where this type of convergence had not been previously established.

math.PR↗