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We study the problem of sampling from a probability distribution on R^p defined via a convex and smooth potential function. We consider a continuous-time diffusion-type process, termed Penalized Langevin dynamics (PLD), the drift of which is the negative gradient of the potential plus a linear penalty that vanishes when time goes to infinity. An upper bound on the Wasserstein-2 distance between the distribution of the PLD at time t and the target is established. This upper bound highlights thearXiv:2006.13998v1 fatcat:ffkgkl4pfbed3larncmr5sx2jq