We study the emptiness formation probability (EFP) in interacting one-dimensional Bose liquids, which is the probability that a snapshot of its ground state reveals exactly zero particles within the interval |x|<R. For a weakly interacting liquid there is parametrically wide regime n-1<R<ζ (here n is the average density and ζ is the healing length) where EFP exhibits a nontrivial crossover from the Poisson to the Gaussian behavior. We employ the instanton technique [NATO Science Series II: Mathematics, Physics and Chemistry (2004), Vol. 221] to study quantitative details of these regime and compare it with previously reported special cases.
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We are indebted to A. Abanov, D. Gangardt, and B. Meerson for valuable discussions. This work was supported by NSF Grant No. DMR-1608238.