We study the statistics of relative distances R(t) between fluid particles in a spatially smooth random flow with arbitrary temporal correlations. Using the space dimensionality d as a large parameter we develop an effective description of Lagrangian dispersion. We describe the exponential growth of relative distances <R 2(t)>∝ exp 2 λ¯t at different values of the ratio between the correlation and turnover times. We find the stretching correlation time which determines the dependence of R1R2 on the difference t1- t2. The calculation of the next cumulant of R2 shows that statistics of R2 is nearly Gaussian at small times (as long as d≫1) and becomes log-normal at large times when large-d approach fails for high-order moments. The crossover time between the regimes is the stretching correlation time which surprisingly appears to depend on the details of the velocity statistics at t≪ τ. We establish the dispersion of the ln( R2) in the log-normal statistics.