capital condensation in the product space and its time scale demonstrate that our model can be a framework for analyzing the evolution of the share distribution at present and in the future. Its limitations is, however, worthy to note. Most of all, we considered a fixed number, 508, of products traded consistently over the studied period 1962-2000. But in reality, new and old products may enter and leave the space of products, which can make big effects. For instance, the critical density $\rho_c$ will be larger with larger $N$, possibly occurring by the rise of new industries. It might pull the international trade out of the pseudo-condensate phase. Also, annual gains $\Delta A$ show large fluctuations for products having small share $A$. Allowing larger chance of gain to small-share, probably new, products might help prevent the condensation of share onto top popular products.

Probabilistic prediction for individual products {#sec:individual}
================================================

![Predictability of individual products’ shares. (a) Scatter plots of unpredictability $U_p$ and mean excess growth rate $\langle R_p\rangle=T^{-1}\sum_t R_p(t)$. Blue and red color are used to represent predictable and unpredictable products with the threshold for significance $U_{\rm crit}=0.094$. (b) The mean excess growth rates of 66 product categories, aggregated by 