Figure 6. Non-stationarity in the characteristic growth fluctuation of word use.

The standard deviation σ_r(t|f_c) of the logarithmic growth rate r_i(t) is presented for all examined corpora. There is an overall decreasing trend arising from the increasing size of the corpora, as depicted in Fig. 5(A). On the other hand, the steady production of new words, as depicted in Fig. 5(B) counteracts this effect. We calculate σ_r(t|f_c) using the relatively common words that meet the criterion that their average word use 〈f_i〉 over the entire word history T_i (using words with lifetime T_i ≥ 10 years) is larger than a threshold f_c ≡ 1/Min[N_u(t)] (see Table I).