We present a comprehensive data description for Ks-band measurements of Sgr A*. We characterize the statistical properties of the variability of Sgr A* in the near-infrared, which we find to be consistent with a single-state process forming a power-law distribution of the flux density. We discover a linear rms-flux relation for the flux-density range up to 12 mJy on a timescale of 24 minutes. This and the power-law flux density distribution implies a phenomenological, formally non-linear statistical variability model with which we can simulate the observed variability and extrapolate its behavior to higher flux levels and longer timescales. We present reasons why data with our cadence cannot be used to decide on the question whether the power spectral density of the underlying random process shows more structure at timescales between 25 min and 100 min compared to what is expected from a red noise random process.

Context. There are a number of faint compact infrared excess sources in the central stellar cluster of the Milky Way. Their nature and origin is unclear. In addition to several isolated objects of this kind there is a small but dense cluster of comoving sources (IRS13N) located ∼3 west of SgrA* just 0.5 north of the bright IRS13E cluster of Wolf-Rayet and O-type stars. Based on the analysis of their color and brightness, there are two main possibilities: (1) they may be dust-embedded stars older than a few Myr; or (2) very young, dusty stars with ages younger than 1 Myr. Aims. We present a first K s -band identification and proper motions of the IRS13N members, the high-velocity dusty S-cluster object (DSO, also referred to as G2), and other infrared excess sources in the central field. Goal is to constrain the nature of these source. Methods. The L -(3.8 μm) K s -(2.2 μm) and H-band (1.65 μm) observations were carried out using the NACO adaptive optics system at the ESO VLT. Proper motions were obtained by linear fitting of the stellar positions extracted by StarFinder as a function of time, weighted by positional uncertainties, and by Gaussian fitting from high-pass filtered and deconvolved images. We also present results of near-infrared (NIR) H-and K s -band ESO-SINFONI integral field spectroscopy of the Galactic center cluster ISR13N. Results. We show that within the uncertainties, the positions and proper motions of the IRS13N sources in K s -and L -band are identical. The HK−sL colors then indicate that the bright L -band IRS13N sources are indeed dust-enshrouded stars rather than core-less dust clouds. The proper motions also show that the IRS13N sources are not strongly gravitationally bound to each other. Combined with their NIR colors, this implies that they have been formed recently. For the DSO we obtain proper motions and a K s -L -color. Conclusions. Most of the compact L -band excess emission sources have a compact H-or K s -band counterpart and therefore are likely stars with dust shells or disks. Our new results and orbital analysis from our previous work favor the hypothesis that the infrared excess IRS13N members and other dusty sources close to SgrA* are young dusty stars and that star formation at the Galactic center (GC) is a continuously ongoing process. For the DSO the color information indicates that it may be a dust cloud or a dust-embedded star.

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