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Motivated by the problem of matching vertices in two correlatedErd\H{o}s-R\'enyi graphs, we study the problem of matching two correlatedGaussian Wigner matrices. We propose an iterative matching algorithm, whichsucceeds in polynomial time as long as the correlation between the two Gaussianmatrices does not vanish. Our result is the first polynomial time algorithmthat solves a graph matching type of problem when the correlation is anarbitrarily small constant.

A polynomial time iterative algorithm for matching Gaussian matrices with non-vanishing correlation