  We study fluctuations in the atom number difference between two halves of a
harmonically trapped Bose gas in three dimensions. We solve the problem
analytically for non interacting atoms. In the interacting case we find an
analytical solution in the Thomas-Fermi and high temperature limit in good
agreement with classical field simulations. In the large system size limit,
fluctuations in the number difference are maximal for a temperature $T\simeq
0.7 T_c$ where $T_c$ is the critical temperature, independently of the trap
anisotropy. The occurrence of this maximum is due to an interference effect
between the condensate and the non-condensed field.
