Christoffel deformation of a measure on the real line consists of multipying
    this measure by a squared polynomial having its roots in $\R$. We introduce
    Christoffel deformations of discrete orthogonal polynomial ensembles by
    considering the Christoffel deformations of the underlying measure, and prove
    that this construction extends to more general point processes describing
    distribution on partitions: the poissonized Plancherel measure and the
    $z$-measures. These deformations contain the theory of Palm measures, and for
    example, explicit formulas for the Palm measures of the poissonized Plancherel
    measure provide a description of the TASEP with initial wedge condition with
    frozen particles. We also obtain new formulas for Palm measures of the
    $z$-measures. The extension to the Plancherel measure is obtained via a limit
    transition from the Charlier ensemble, while the extension to the $z$-measures
    follows from an analytic continuation argument. A limit procedure starting from
    the non-degenerate $z$-measures leads to a deformation of the Gamma process
    introduced by Borodin and Olshanski.

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