数物系科学拠点では、2023年9月26日（火）と27日（水）に、国際教育活動の一環として標記特別講義を開催します。Ofer Zeitouni先生と阿部圭宏先生を講演者にお迎えし、ガウス自由場と関連するトピックスについてご講演いただく予定です。
講義タイトル
『ガウス自由場とその周辺（Gaussian free fields and related topics）』 特別講義
日程
2023年9月26日（火）
- 14:30-16:10 阿部圭宏（東北大学大学院理学研究科 准教授）
- 16:30-18:30 Ofer Zeitouni (Weizmann Institute of Science and New York University, Professor)
2023年9月27日（水）
- 14:30-16:10 阿部圭宏（東北大学大学院理学研究科 准教授）
- 16:10-16:30 Coffee Break
- 16:30-18:30 Ofer Zeitouni (Weizmann Institute of Science and New York University, Professor)
講師
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Ofer Zeitouni先生Weizmann Institute of Science and New York University, Professor 講演テーマ：Extreme value theory for 2D Gaussian free field and logarithmically correlated fields |
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阿部圭宏先生講演テーマ：Discrete Gaussian free fields and its applications to random walks |
会場
早稲田大学西早稲田キャンパス63号館2階05会議室（アクセス）およびZoomによるハイブリッド開催
言語
英語
対象
研究者、学生
事前登録
事前登録が必要です。参加を希望される方は、こちらから参加登録をお願いします。
お問合せ
【講義内容等に関するお問合わせ】
早稲田大学基幹理工学部数学科 熊谷隆 教授 t-kumagai［at］waseda.jp
【参加登録等に関するお問合せ】
SGU数物系科学拠点 info [at] sgu-mathphys.sci.waseda.ac.jp
タイムテーブル ※質疑応答時間を含む
9月26日（火）
14:30 – 16:10 |
阿部圭宏 准教授（東北大学大学院理学研究科）
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| （講義概要） The discrete Gaussian free field (DGFF) is a centered Gaussian field on a graph whose covariance is given by the inverse of the graph Laplacian. It is a probabilistic model of interfaces and has connections with a lot of other models such as local times of random walks and branching random walks. In the first half of this lecture, I will give some motivation and basics of DGFF such as the random walk representation and the domain Markov property. In the second half, I will review some progress on the extreme value theory of DGFF on the integer lattice in three or higher dimensions. |
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16:30 – 18:30 |
Ofer Zeitouni 教授 (Weizmann Institute of Science and New York University)
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| （講義概要） The extreme value theory for Gaussian logarithmically correlated fields (G-LCFs) has emerged in the last decade as a powerful tool in the analysis of interface models, quantum gravity, random matrices and in a myriad of other applications. The two dimensional Gaussian free field (and its discrete analogue) is an important motivating example of such a field. In this lecture, I will describe the relation and differences between the extreme value theory for i.i.d. variables and that for G.-LCFs, and introduce the relation with branching structures and various tools such as comparison theorems, scale decompositions and relations to branching random walks. |
9月27日（水）
14:30 – 16:10 |
阿部圭宏 准教授（東北大学大学院理学研究科）
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| （講義概要） The discrete Gaussian free field (DGFF) and the simple random walk (SRW) have a close relationship via the generalized second Ray-Knight theorem, which is a distributional identity between the square of DGFF and the local time of SRW. Thanks to the theorem, we have witnessed rapid progress on the studies of the cover time (the first time at which SRW visits all the vertices) and thick points of SRW (sites frequently visited by SRW). In the first half of this lecture, I will state the generalized second Ray-Knight theorem and review results on the cover time due to Ding-Lee-Peres (2012) and Zhai (2018) where we can see beautiful applications of the theorem. In the second half, I will focus on applications to thick points of SRW. |
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16:30 – 18:30 |
Ofer Zeitouni 教授 (Weizmann Institute of Science and New York University)
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| （講義概要） In the first lecture we discussed extreme value theory for logarithmically correlated Gaussian fields. In this talk I will discuss what changes in the non-Gaussian Gaussian setup. A prime example is the study of cover time of certain planar graphs or two dimensional manifolds by random walk or Brownian motion. In spite of precise and beautiful links through isomorphism theorems, the question about the cover time of the 2D torus by a Wiener sausage (or its discrete analogue) requires new tools. I will describe some work, old and recent, on this question, culminating with limit theorems for the cover time. If time permits, I will briefly discuss other types of non Gaussian LCFs. |
