| Full text | |
| Author(s): |
Abadi, Miguel
;
Lambert, Rodrigo
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Ergodic Theory and Dynamical Systems; v. 39, p. 16-pg., 2019-07-01. |
| Abstract | |
We consider two independent and stationary measures over chi(N), where chi is a finite or countable alphabet. For each pair of n-strings in the product space we define T-n((2)) as the length of the shortest path connecting one of them to the other. Here the paths are generated by the underlying dynamic of the measures. If they are ergodic and have positive entropy we prove that, for almost every pair of realizations (x, y), T-n((2))/n is concentrated in one, as n diverges. Under mild extra conditions we prove a large-deviation principle. We also show that the fluctuations of T-n((2)) converge (only) in distribution to a non-degenerate distribution. These results are all linked to a quantity that computes the similarity between those two measures. This is the so-called divergence between two measures, which is also introduced. Several examples are provided. (AU) | |
| FAPESP's process: | 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat |
| Grantee: | Oswaldo Baffa Filho |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |
| FAPESP's process: | 14/19805-1 - Statistics of extreme events and dynamics of recurrence |
| Grantee: | Miguel Natalio Abadi |
| Support Opportunities: | Regular Research Grants |