This paper studies how large fluctuations in the early universe are spatially correlated due to quantum diffusion during inflation. Using the stochastic-δN formalism, the authors derive an exact description of physical distances measured by a local observer at the end of inflation, improving upon previous works. They propose a "large-volume" approximation, allowing calculations using first-passage time analysis and derive a new formula for the power spectrum in stochastic inflation. The study of two-point statistics of curvature perturbations reveals that the joint distribution of large fluctuations is of the form P(ζR1, ζR2) = F(R1, R2, r)P(ζR1)P(ζR2), indicating that the reduced correlation function is independent of the threshold value ζc. This contrasts with Gaussian statistics, where the same quantity strongly decays with ζc, showing the existence of a universal clustering profile for all structures forming in the exponential tails. Structures forming in the intermediate tails may exhibit different, model-dependent behaviors. The paper also discusses the implications of non-Gaussianities on PBH clustering, showing that they deeply alter clustering compared to Gaussian statistics. The authors use the stochastic-δN formalism to compute PBH clustering in the presence of non-perturbative non-Gaussianities, showing that the main conclusions from toy models are generic. The paper concludes that the stochastic-δN formalism is necessary to derive the expected statistics of PBHs, as they are directly sensitive to the heavy tails of the distribution.This paper studies how large fluctuations in the early universe are spatially correlated due to quantum diffusion during inflation. Using the stochastic-δN formalism, the authors derive an exact description of physical distances measured by a local observer at the end of inflation, improving upon previous works. They propose a "large-volume" approximation, allowing calculations using first-passage time analysis and derive a new formula for the power spectrum in stochastic inflation. The study of two-point statistics of curvature perturbations reveals that the joint distribution of large fluctuations is of the form P(ζR1, ζR2) = F(R1, R2, r)P(ζR1)P(ζR2), indicating that the reduced correlation function is independent of the threshold value ζc. This contrasts with Gaussian statistics, where the same quantity strongly decays with ζc, showing the existence of a universal clustering profile for all structures forming in the exponential tails. Structures forming in the intermediate tails may exhibit different, model-dependent behaviors. The paper also discusses the implications of non-Gaussianities on PBH clustering, showing that they deeply alter clustering compared to Gaussian statistics. The authors use the stochastic-δN formalism to compute PBH clustering in the presence of non-perturbative non-Gaussianities, showing that the main conclusions from toy models are generic. The paper concludes that the stochastic-δN formalism is necessary to derive the expected statistics of PBHs, as they are directly sensitive to the heavy tails of the distribution.