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We study the distribution of particle number in extended subsystems of aone-dimensional non-interacting Fermi gas confined in a potential well at zerotemperature. Universal features are identified in the scaled bulk and edgeregions of the trapped gas where the full counting statistics are given by thecorresponding limits of the eigenvalue statistics in Gaussian unitary randommatrix ensembles. The universal limiting behavior is confirmed by the bulk andedge scaling of the particle number fluctuations and the entanglement entropy.

Universality in the full counting statistics of trapped fermions