Denker, Manfred 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. Reviewer: Chen Mu-fa (Beijing) Cited in 7 Documents MSC: 60F10 Large deviations 60K35 Interacting random processes; statistical mechanics type models; percolation theory Keywords:measure preserving transformation; Gibbs measure; increments of the pressure functions Citations:Zbl 0752.00047 PDFBibTeX XMLCite \textit{M. Denker}, in: Information theory, statistical decision functions, random processes. Transactions of the 11th Prague conference, held from August 27-31, 1990 in Prague, Czechoslovakia. Volume A. Dordrecht: Kluwer Academic Publishers. 21--33 (1992; Zbl 0769.60025)