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Computer-mediated communication is driving fundamental changes in the nature of written language. We investigate these changes by statistical analysis of a dataset comprising 107 million Twitter messages (authored by 2.7 million unique user accounts). Using a latent vector autoregressive model to aggregate across thousands of words, we identify high-level patterns in diffusion of linguistic change over the United States. Our model is robust to unpredictable changes in Twitter's sampling rate, and provides a probabilistic characterization of the relationship of macro-scale linguistic influence to a set of demographic and geographic predictors. The results of this analysis offer support for prior arguments that focus on geographical proximity and population size. However, demographic similarity - especially with regard to race - plays an even more central role, as cities with similar racial demographics are far more likely to share linguistic influence. Rather than moving towards a single unified "netspeak" dialect, language evolution in computer-mediated communication reproduces existing fault lines in spoken American English.