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Date | 2022-11-25 |
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Speaker | 이중경 |

Dept. | 서울대학교 |

Room | 27-220 |

Time | 15:00-16:00 |

In this thesis, we investigated the metastability of non-reversible Langevin dynamics.

The first topic is the precise estimation of the expectation of transition time, which is called the Eyring-Kramers formula. Compared to the gradient model, our result reveals that the metastable transition of the non-reversible dynamics occurs faster than that of the reversible ones. Proof of the Eyring-Kramer formula is based on a potential theoretic approach estimating the capacity between metastable valleys. We developed a novel method to estimate capacity without relying on variational principles such as Dirichlet's and Thomson's principles. In addition, we also explain the Markov chain model reduction of the non-reversible dynamics which provides the full description of successive transitions when there are multiple global minima.

Finally, we introduce the analysis of the energy landscape of the Curie-Weiss-Potts model which is an example of a dynamics on complex potential function so that complex metastability investigated above indeed occurs.

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