We analyze the statistical properties and dynamical implications of galaxy distributions in phase space for samples selected from the 2MASS Extended Source Catalog. The galaxy distribution is decomposed into modes $\delta({ \bf k, x})$ which describe the number density perturbations of galaxies in phase space cell given by scale band $\bf k$ to ${ \bf k}+\Delta { \bf k}$ and spatial range $\bf x$ to ${ \bf x}+\Delta { \bf x}$. In the nonlinear regime, $\delta({ \bf k, x})$ is highly non-Gaussian. We find, however, that the correlations between $\delta({ \bf k, x})$ and $\delta({ \bf k', x'})$ are always very weak if the spatial ranges (${ \bf x}$, ${ \bf x}+\Delta { \bf x}$) and (${ \bf x'}$, ${ \bf x'}+\Delta { \bf x'}$) don't overlap. This feature is due to the fact that the spatial locality of the initial perturbations is memorized during hierarchical clustering. The highly spatial locality of the 2MASS galaxy correlations is a strong evidence for the initial perturbations of the cosmic mass field being spatially localized, and therefore, consistent with a Gaussian initial perturbations on scales as small as about 0.1 h$^{ -1}$ Mpc. Moreover, the 2MASS galaxy spatial locality indicates that the relationship between density perturbations of galaxies and the underlying dark matter should be localized in phase space. That is, for a structure consisting of perturbations on scales from $k$ to $ k+\Delta { k}$, the nonlocal range in the relation between galaxies and dark matter should { \it not} be larger than $|{ \Delta { \bf x}}|=2\pi/|\Delta { \bf k}|$. The stochasticity and nonlocality of the bias relation between galaxies and dark matter fields should be no more than the allowed range given by the uncertainty relation $|{ \Delta { \bf x}|| \Delta{ \bf k}}|=2\pi$.
Categories: astro-ph