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ファイル | 記述 | サイズ | フォーマット | |
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B59-13.pdf | 5.15 MB | Adobe PDF | 見る/開く |
タイトル: | Characterizations of the hydrodynamic limit of the Dyson model (Stochastic Analysis on Large Scale Interacting Systems) |
著者: | Andraus, Sergio Katori, Makoto |
著者名の別形: | カトリ, マコト |
キーワード: | 82C22 15B52 35Q31 44A15 Interacting Brownian motions Dyson model Hydrodynamic limit Hilbert transform Green's function Method of characteristics |
発行日: | Jul-2016 |
出版者: | Research Institute for Mathematical Sciences, Kyoto University |
誌名: | 数理解析研究所講究録別冊 |
巻: | B59 |
開始ページ: | 157 |
終了ページ: | 173 |
抄録: | Under appropriate conditions for the initial configuration, the empirical measure of the N-particle Dyson model with parameter β ≥ 1 converges to a unique measure-valued process as N goes to infinity, which is independent of β. The limit process is characterized by its Stieltjes transform called the Green's function. Since the Green's function satisfies the complex Burgers equation in the inviscid limit, this is called the hydrodynamic limit of the Dyson model. We review the relations among the hydrodynamic equation of the Green's function, the continuity equation of the probability density function, and the functional equation of the Green's function. The basic tools to prove the relations are the Hilbert transform, a special case of the Sokhotski-Plemelj theorem, and the method of characteristics for solving partial differential equations. For two special initial configurations, we demonstrate how to characterize the limit processes using these relations. |
記述: | "Stochastic Analysis on Large Scale Interacting Systems". October 26~29, 2015. edited by Ryoki Fukushima, Tadahisa Funaki, Yukio Nagahata, Makoto Nakashima, Hirofumi Osada and Yoshiki Otobe. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. |
著作権等: | © 2016 by the Research Institute for Mathematical Sciences, Kyoto University. All rights reserved. |
URI: | http://hdl.handle.net/2433/243600 |
出現コレクション: | B59 Stochastic Analysis on Large Scale Interacting Systems |
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