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We apply the theorems from the theory of Toeplitz determinants to calculatethe asymptotics of various correlators including the exponential ones in theinpenetrable one-dimensional Bose gas system. The known correlators in thefree-fermion system are also used to test the generalized Fisher-Hartwigconjecture.

Fisher-Hartwig conjecture and the correlators in the inpenetrable Bose gas