  Spontaneously created vortex-antivortex pairs are the predominant source of
flux noise in high-temperature superconductors. In principle, flux noise
measurements allow to check theoretical predictions for both the distribution
of vortex-pair sizes and for the vortex diffusivity. In this paper the
flux-noise power spectrum is calculated for the highly anisotropic
high-temperature superconductor Bi-2212, both for bulk crystals and for
ultra-thin films. The spectrum is basically given by the Fourier transform of
the temporal magnetic-field correlation function. We start from a
Berezinskii-Kosterlitz-Thouless type theory and incorporate vortex diffusion,
intra-pair vortex interaction, and annihilation of pairs by means of a
Fokker-Planck equation to determine the noise spectrum below and above the
superconducting transition temperature. We find white noise at low frequencies
omega and a spectrum proportional to 1/omega^(3/2) at high frequencies. The
cross-over frequency between these regimes strongly depends on temperature. The
results are compared with earlier results of computer simulations.
