GaAs layers grown by molecular beam epitaxy at low temperatures (LT GaAs) have several interesting properties. For example, concentrations up to 2 × 10^{20} cm^{-3} of neutral and up to 5 × 10^{18} cm^{-3} of positively charged As_{Ga} defects have been determined in as grown layers. It has been observed that electrical transport in LT GaAs is dominated by hopping conductivity. In the as grown and annealed up to 400°C layers, experiments show a high mobility of photo-excited electrons up to 20000 cm^{2}/(V s) at about 130 K. Taking into account the very high concentration of ionized defects in LT GaAs, the best possible explanation of the measured value of mobility is an assumption that As^{+}_{Ga} defects interact with ionized acceptors A¯. This leads to creation of As^{+}_{Ga}-A¯ dipoles, which do not scatter electrons as efficiently as single ions. It has been shown that the donor-acceptor correlation could be destroyed by illumination which ionizes As_{Ga} defects. Also analysis of hopping conductivity suggests the existence of the donor-acceptor correlations in non-illuminated LT GaAs. Numerical calculation of As_{Ga}-acceptors interaction has been done. It shows that at least below 200 K dipole formation in LT GaAs is possible and could lead to observed increase in mobility.