This article presents experimental findings on anyonic statistics and slow quasiparticle dynamics in a monolayer graphene Fabry-Pérot interferometer at the fractional quantum Hall state ν = 1/3. The study focuses on measuring the anyonic exchange phase θ_a, which is a key feature of anyonic statistics. The researchers observed phase slips in the interference pattern, which are attributed to the tunneling of quasiparticles into the interferometer. The magnitude of these phase slips was found to be approximately 2π/3, consistent with previous experiments in GaAs quantum wells and theoretical expectations for Abelian anyons. The study also reveals that quasiparticle equilibration times can be long, up to 20 minutes, which affects the measurement of the interferometer phase. The researchers used the discrepancy between the quasiparticle equilibration rate and their measurement speed to independently vary the interferometer area and the number of quasiparticles, allowing precise determination of the interferometer phase and monitoring of individual anyon entry and exit. The results demonstrate that the average 'topological charge' of a mesoscopic quantum Hall device can be maintained over extended timescales. The study also shows that the phase slips are not always quantized, suggesting that some impurity sites may trap quasiparticles near the edge. The observed phase slips are interpreted as the entry of single e/3 anyons into the interferometer. The slow quasiparticle dynamics observed in this system open new possibilities for studying the physics of fractionalized phases at the single anyon level. The results suggest that the long timescales for charge motion may enable the detection of non-Abelian statistics in future experiments. The study provides a detailed analysis of the interferometer's behavior and the dynamics of quasiparticles in the ν = 1/3 state, contributing to the broader understanding of quantum Hall systems and anyonic statistics.This article presents experimental findings on anyonic statistics and slow quasiparticle dynamics in a monolayer graphene Fabry-Pérot interferometer at the fractional quantum Hall state ν = 1/3. The study focuses on measuring the anyonic exchange phase θ_a, which is a key feature of anyonic statistics. The researchers observed phase slips in the interference pattern, which are attributed to the tunneling of quasiparticles into the interferometer. The magnitude of these phase slips was found to be approximately 2π/3, consistent with previous experiments in GaAs quantum wells and theoretical expectations for Abelian anyons. The study also reveals that quasiparticle equilibration times can be long, up to 20 minutes, which affects the measurement of the interferometer phase. The researchers used the discrepancy between the quasiparticle equilibration rate and their measurement speed to independently vary the interferometer area and the number of quasiparticles, allowing precise determination of the interferometer phase and monitoring of individual anyon entry and exit. The results demonstrate that the average 'topological charge' of a mesoscopic quantum Hall device can be maintained over extended timescales. The study also shows that the phase slips are not always quantized, suggesting that some impurity sites may trap quasiparticles near the edge. The observed phase slips are interpreted as the entry of single e/3 anyons into the interferometer. The slow quasiparticle dynamics observed in this system open new possibilities for studying the physics of fractionalized phases at the single anyon level. The results suggest that the long timescales for charge motion may enable the detection of non-Abelian statistics in future experiments. The study provides a detailed analysis of the interferometer's behavior and the dynamics of quasiparticles in the ν = 1/3 state, contributing to the broader understanding of quantum Hall systems and anyonic statistics.