Existence of Large deviations rate function for any S-unimodal map

2019/08/21 by Hiroki Takahasi, Takahasi, Hiroki, Masato Tsujii +1 · 2 citations
Mathematics · Physics and Astronomy · #37A50 #37D20 #37D25 #37D35 #37E05 #37E20 #Critical point (mathematics) #Dynamical Systems (math.DS) #FOS: Mathematics #Function (biology) #Geometry #Large deviations theory #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Point (geometry) #Quantum chaos and dynamical systems #Rate function #Schwarzian derivative #Statistics #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1908.07716

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2019/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For an arbitrary negative Schwarzian unimodal map with non-flat critical point, we establish the level-2 Large Deviation Principle (LDP) for empirical distributions. We also give an example of a multimodal map for which the level-2 LDP does not hold.

Citations

• GIBBS MEASURES IN ERGODIC THEORY
• Quantitative universality for a class of nonlinear transformations

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