This PhD project aims to develop an innovative method to characterize the reactivity of fissile systems by analyzing their stochastic fluctuations, known as zero-power neutron noise. In a subcritical fissile medium, neutrons originating from spontaneous fission can initiate short and random chain reactions, generating a fluctuating signal. This noise carries essential information on the distance of the system to criticality, a key parameter both for the safety of nuclear installations (prevention of criticality accidents) and for the detection of undeclared fissile materials (nuclear security and non-proliferation).

Existing theoretical approaches to infer system reactivity from neutron noise are limited to idealized situations and become unsuitable in realistic configurations, particularly when the system is strongly subcritical or when significant uncertainties exist regarding its geometry or composition (as in the case of the Fukushima Daiichi corium or spent fuel storage). Monte Carlo simulations then appear as a natural alternative, but current simulations rely on variance reduction techniques that fail to correctly preserve stochastic fluctuations.

This thesis proposes to address this scientific challenge by adapting a relatively recent variance reduction method known as Adaptive Multilevel Splitting (AMS), originally developed to efficiently sample rare events while preserving their statistical properties. The goal is to extend this method to neutron transport in multiplying media and to make it a tool capable of faithfully simulating the temporal correlations characteristic of neutron noise. Following the theoretical developments, the algorithm will be implemented in Geant4, compared to analytical benchmark solutions, and experimentally validated through in situ measurements (using neutron sources or research reactors). In the long term, this work may lead to direct applications in nuclear monitoring, safety diagnostics, and detector physics, while also opening perspectives in fundamental physics and medical physics.