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Large deviations and the pressure function. (English) Zbl 0769.60025
Information theory, statistical decision functions, random processes, Trans. 11th Prague Conf., Prague/Czech. 1990, Vol. A, 21-33 (1992).
[For the entire collection see Zbl 0752.00047.]
This note studies the large deviations for the dynamics $$\sum^{n- 1}_{i=0}g\circ T^ i$$, where $$T$$ is a measure preserving transformation. It is proved that for Gibbs measure, the information function can be described by the pressure function. Moreover, a lower bound for the increments of the pressure functions is also presented.

##### MSC:
 60F10 Large deviations 60K35 Interacting random processes; statistical mechanics type models; percolation theory