Exponential estimates for plurisubharmonic functions and stochastic dynamics

Tien-Cuong Dinh Institut de Math´ematiques de Jussieu Viˆet-Anh Nguyˆen Universit´e Paris-Sud Nessim Sibony Universit´e Paris-Sud

Differential Geometry mathscidoc:1609.10170

Journal of Differential Geometry, 84, (3), 465-488, 2010
We prove exponential estimates for plurisubharmonic functions with respect to Monge-Amp`ere measures with H¨older continuous potential. As an application, we obtain several stochastic properties for the equilibrium measures associated to holomorphic maps on projective spaces. More precisely, we prove the exponential decay of correlations, the central limit theorem for general d.s.h. observables, and the large deviations theorem for bounded d.s.h. observables and H¨older continuous observables.
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@inproceedings{tien-cuong2010exponential,
  title={EXPONENTIAL ESTIMATES FOR PLURISUBHARMONIC FUNCTIONS AND STOCHASTIC DYNAMICS},
  author={Tien-Cuong Dinh, Viˆet-Anh Nguyˆen, and Nessim Sibony},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911213230126142827},
  booktitle={Journal of Differential Geometry},
  volume={84},
  number={3},
  pages={465-488},
  year={2010},
}
Tien-Cuong Dinh, Viˆet-Anh Nguyˆen, and Nessim Sibony. EXPONENTIAL ESTIMATES FOR PLURISUBHARMONIC FUNCTIONS AND STOCHASTIC DYNAMICS. 2010. Vol. 84. In Journal of Differential Geometry. pp.465-488. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911213230126142827.
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