The Laser Interferometer Gravitational-wave Observatory ( LIGO ) has performed the fourth science run , S4 , with significantly improved interferometer sensitivities with respect to previous runs .
Using data acquired during this science run , we place a limit on the amplitude of a stochastic background of gravitational waves .
For a frequency independent spectrum , the new limit is \Omega _ { GW } < 6.5 \times 10 ^ { -5 } .
This is currently the most sensitive result in the frequency range 51-150 Hz , with a factor of 13 improvement over the previous LIGO result .
We discuss complementarity of the new result with other constraints on a stochastic background of gravitational waves , and we investigate implications of the new result for different models of this background .