2016/11/04 by Miguel Abadi, Abadi, Miguel, Rodrigo Lambert +1 · 1 citation
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #Cellular Automata and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1611.01530
We consider two independent and stationary measures over \χ^\ℕ,\nwhere \χ finite or countable alphabet. For each pair of n-strings in the\nproduct space we define Tn(2) as the length of the shortest path\nconnecting one string to the other where the paths are generating by the\nunderlying dynamics of the measure. For ergodic measures with positive entropy\nwe prove that, for almost every pair of realizations (x,y), T(2)n/n\nconcentrates in one, as n diverges. Under mild extra conditions we prove a\nlarge deviation principle. This principle is linked to a quantity that compute\nthe similarity between the two measures that we also introduce. We further\nprove its existence and other properties. We also show that the fluctuations of\nTn(2) converge (only) in distribution to a non-degenerated distribution.\nSeveral examples are provided for all results.\n