Probability Measure Near the Boundary of Tensor Power Decomposition for so2n+1

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Character measure is a probability measure on irreducible representations of a semisimple Lie algebra. It appears from the decomposition into irreducibles of tensor power of a fundamental representation. In this paper we calculate the asymptotics of character measure on representations of so2n+1 in the regime near the boundary of weight diagram. We find out that it converges to a Poisson-type distribution.