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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

From the divergence between two measures to the shortest path between two observables

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Abadi, Miguel [1] ; Lambert, Rodrigo [2]
Total Authors: 2
[1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil
[2] Univ Fed Uberlandia, Fac Matemat, Av Joao Naves de Avila 2121, BR-38408100 Uberlandia, MG - Brazil
Total Affiliations: 2
Document type: Journal article
Source: Ergodic Theory and Dynamical Systems; v. 39, n. 7, p. 1729-1744, JUL 2019.
Web of Science Citations: 1

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: 14/19805-1 - Statistics of extreme events and dynamics of recurrence
Grantee:Miguel Natalio Abadi
Support type: Regular Research Grants
FAPESP's process: 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat
Grantee:Jefferson Antonio Galves
Support type: Research Grants - Research, Innovation and Dissemination Centers - RIDC