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The Parabolic Anderson Model : Random Walk in Random Potential / by Wolfgang König
(Pathways in Mathematics. ISSN:2367346X)
版 | 1st ed. 2016. |
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出版者 | Cham : Springer International Publishing : Imprint: Birkhäuser |
出版年 | 2016 |
大きさ | XI, 192 p. 4 illus : online resource |
著者標目 | *König, Wolfgang author SpringerLink (Online service) |
件 名 | LCSH:Probabilities LCSH:Mathematical physics FREE:Probability Theory FREE:Mathematical Physics FREE:Mathematical Methods in Physics |
一般注記 | 1 Background, model and questions -- 2 Tools and concepts -- 3 Moment asymptotics for the total mass -- 4 Some proof techniques -- 5 Almost sure asymptotics for the total mass -- 6 Strong intermittency -- 7 Refined questions -- 8 Time-dependent potentials This is a comprehensive survey on the research on the parabolic Anderson model – the heat equation with random potential or the random walk in random potential – of the years 1990 – 2015. The investigation of this model requires a combination of tools from probability (large deviations, extreme-value theory, e.g.) and analysis (spectral theory for the Laplace operator with potential, variational analysis, e.g.). We explain the background, the applications, the questions and the connections with other models and formulate the most relevant results on the long-time behavior of the solution, like quenched and annealed asymptotics for the total mass, intermittency, confinement and concentration properties and mass flow. Furthermore, we explain the most successful proof methods and give a list of open research problems. Proofs are not detailed, but concisely outlined and commented; the formulations of some theorems are slightly simplified for better comprehension HTTP:URL=https://doi.org/10.1007/978-3-319-33596-4 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783319335964 |
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EB00206008 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA273.A1-274.9 DC23:519.2 |
書誌ID | 4000118848 |
ISBN | 9783319335964 |
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※2017年9月4日以降