Different authors meant somewhat different things by "random walk," but the most common meaning was that "successive price changes are independent, identically distributed random variables. Most simply, this implies that the series of price changes has no memory, that is, the past cannot be used to predict the future in any meaningful way." (Fama 1965, p. 34) That property implied "weak form" efficiency. However, the latter was also implied by martingale ("fair game") models that were more general than the original conception of random walks. After these martingale formulations were introduced in the mid 1960s by Samuelson (and also by Benoit Mandelbrot) they tended to replace random walks as the preferred mathematical formulations of weakform efficiency.

Donald MacKenzie, An Engine, Not a Camera, loc. 293