Fluctuations of K-band galaxy counts

We measure the variance in the distribution of off-plane (|b|>20 deg.) galaxies with m_K<13.5 from the 2MASS K-band survey in circles of diameter between 0.344 deg. and 57.2 deg. The use of a near-infrared survey makes negligible the contribution of Galactic extinction to these fluctuations. We calculate these variances within the standard Lambda-CDM model assuming that the sources are distributed like halos of the corresponding mass, and it reproduces qualitatively the galaxy counts variance. Therefore, we test that the counts can be basically explained in terms only of the large scale structure. A second result of this paper is a new method to determine the two point correlation function obtained by forcing agreement between model and data. This method does not need the knowledge of the two-point angular correlation function, allows an estimation of the errors (which are low with this method), and can be used even with incomplete surveys. Using this method we get xi(z=0, r<10 h^{-1}Mpc)=(29.8+/-0.3) (r/h^{-1}Mpc)^{-1.79+/-0.02}, which is the first measure of the amplitude of xi in the local Universe for the K-band. It is more or less in agreement with those obtained through red optical filters selected samples, but it is larger than the amplitude obtained for blue optical filters selected samples.