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Leppänen Juho　Junior Associate Professor

 

Affiliation

Research Institute of Science and Technology, Tokai University

Contact

E-mail : leppanen@tsc.u-tokai.ac.jp

Degree/ License

Ph.D.

Biography

2015－2018
Ph.D. Candidate,
Department of Mathematics and Statistics,
University of Helsinki (Finland)
2018－2020
Postdoctoral Researcher,
Laboratory of Probability, Statistics, and Modelling, Sorbonne University (France)
2020－2021
Data Scientist, XICA inc. (Japan)
2021－2022
Data Scientist, Welmo inc. (Japan)
2022－Present
東海大学 総合科学技術研究所　特任講師
Junior Associate Professor,
Research Institute of Science and Technology, Tokai University (Japan)

Research Field

I use methods from probability, stochastics, and functional analysis to describe the statistical properties of chaotic systems, i.e. systems that display a sensitive dependence on initial conditions. The term statistical refers to the long-term behavior of trajectories of such systems, e.g., the limiting behavior of time series arising as observations along the trajectory, frequencies of deviations from these limits, etc.

Most of my research so far has dealt with probabilistic limit laws, such as central limit theorems and concentration inequalities, associated to partial sums of (piecewise) smooth uniformly and non-uniformly hyperbolic systems, with particular focus on non-autonomous and intermittent type dynamics. I have also conducted research related to response theory, which concerns the robustness of statistical properties of dynamical systems subject to perturbations. My ongoing research focuses on obtaining quantitative extensions of certain limit laws for hyperbolic dynamical systems. Such results give concrete estimates on the distance between the underlying process and the limiting distribution.

Keywords

Hyperbolic dynamics, Statistical limit laws, Intermittency, Non-autonomous dynamics, Response theory, Transfer operator

Membership (of Academic Organization)

  • The Mathematical Society of Japan

Message

Dynamical systems theory has found applications in almost all areas of science and technology. A modern example can be found in machine learning, where dynamical systems theory has been useful in improving the interpretability and efficiency of certain algorithms, such as recurrent neural networks used to model sequential data. The machine learning approach becomes important in the case of complex dynamics such as those displayed by the climate or brain, in which case explicit models are hard to construct. I would be highly interested in contributing to such interdisciplinary studies in the future.