In this paper, we consider a deformation of Plantherel measure linked to Jack polynomials. Our main result is the description of the first-and second-order asymptotics of the bulk of a random Young diagram under this distribution, which extends celebrated results of Vershik, Kerov, Logan, and Shepp (for the first-order asymptotics) and Kerov (for the second-order asymptotics). This gives more evidence for the connection with the Gaussian,8-ensemble, already suggested by a work of Matswnoto.
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