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We analyze the non-perturbative structure of the strange sea of the nucleon within a meson cloud picture. In a low approach in which the nucleon is viewed as a three valon bound state, we evaluate the probability distribution of an in-nucleon Kaon-Hyperon pair in terms of splitting functions and recombination. The resulting kaon and hyperon probability densities are convoluted with suitable strange distributions inside the meson and baryon in order to obtain non-perturbative contributions to the strange sea of the nucleon. We find a structured strange/anti-strange asymmetry, displaying a clear excess of quarks (anti-quarks) for large (small) momentum fractions

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