The paper investigates the spatial correlation of large fluctuations in the presence of quantum diffusion during inflation, focusing on the clustering of primordial black holes (PBHs). The authors use the stochastic-$\delta N$ formalism to compute real-space correlation functions, improving upon previous works by deriving an exact description of physical distances measured by a local observer at the end of inflation. They propose a "large-volume" approximation, which allows for the calculation of quantities using first-passage time analysis, and derive a new formula for the power spectrum in stochastic inflation. The study reveals that the joint distribution of large fluctuations follows a specific form, indicating a universal clustering profile for structures forming in the exponential tails. This contrasts with Gaussian statistics, where the reduced correlation function decays with the threshold value. The authors apply their formalism to toy models and discuss how non-Gaussian heavy tails significantly alter clustering compared to Gaussian statistics. The main conclusions are shown to be generic, and the paper concludes with future directions for research.The paper investigates the spatial correlation of large fluctuations in the presence of quantum diffusion during inflation, focusing on the clustering of primordial black holes (PBHs). The authors use the stochastic-$\delta N$ formalism to compute real-space correlation functions, improving upon previous works by deriving an exact description of physical distances measured by a local observer at the end of inflation. They propose a "large-volume" approximation, which allows for the calculation of quantities using first-passage time analysis, and derive a new formula for the power spectrum in stochastic inflation. The study reveals that the joint distribution of large fluctuations follows a specific form, indicating a universal clustering profile for structures forming in the exponential tails. This contrasts with Gaussian statistics, where the reduced correlation function decays with the threshold value. The authors apply their formalism to toy models and discuss how non-Gaussian heavy tails significantly alter clustering compared to Gaussian statistics. The main conclusions are shown to be generic, and the paper concludes with future directions for research.