This thesis investigates the convergence behavior of the fluctuation process associated with the eigenvectors of Wigner matrices. We define a stochastic process constructed from the squared moduli of the eigenvector entries and analyze its convergence in the Skorokhod space D[0,1]. Our main result establishes that, under appropriate normalization and moment conditions, this process converges in distribution to a Brownian bridge. To prove this, we first verify tightness using moment bounds and control of the modulus of continuity. We then apply previous works on the convergence of finite-dimensional distributions. The proofs rely on known results in random matrix theory, including isotropic delocalization and eigenvalue rigidity, and draw on classical probabilistic tools such as the central limit theorem and Donsker’s theorem. This work contributes to the broader understanding of universality phenomena in random matrices, specifically in the behavior of eigenvectors, and highlights the interplay between spectral theory and functional limit theorems.