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We consider $n$ particles $0\leq x_1<x_2< \cdots < x_n < +\infty$, distributed according to a probability measure of the form $$ \frac{1}{Z_n}\prod_{1\leq i <j \leq n}(x_j-x_i)\prod_{1\leq i <j \leq n}(x_j^{\theta}-x_i^{\theta})\prod_{j=1}^nx_j^\alpha e^{-x_j}\ud x_j, ~~ \alpha>-1,~~ \theta>0, $$ where $Z_n$ is the normalization constant.
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