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We consider the point process [Formula presented] where Zn is the normalization constant. The feature of this process is that the points eiθ1,…,eiθn interact with the mirror points reflected over the real line e−iθ1,…,e−iθn. We study smooth linear statistics of the form ∑j=1ng(θj) as n→∞, where g is 2π-periodic. We prove that a wide range of asymptotic scenarios can occur: depending on g, the lead
