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The parabolic Anderson model[electronic resource] :random walk in random potential /

紀錄類型:	書目-電子資源 : Monograph/item
杜威分類號:	519.282
書名/作者:	The parabolic Anderson model : random walk in random potential // by Wolfgang Konig.
作者:	Konig, Wolfgang.
出版者:	Cham : : Springer International Publishing :, 2016.
面頁冊數:	ix, 192 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Random walks (Mathematics)
標題:	Parabolic operators.
標題:	Mathematics.
標題:	Probability Theory and Stochastic Processes.
標題:	Mathematical Applications in the Physical Sciences.
標題:	Mathematical Methods in Physics.
ISBN:	9783319335964
ISBN:	9783319335957
內容註:	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.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-33596-4

The parabolic Anderson model[electronic resource] :random walk in random potential /
Konig, Wolfgang.

The parabolic Anderson modelrandom walk in random potential /[electronic resource] :by Wolfgang Konig. - Cham :Springer International Publishing :2016. - ix, 192 p. :ill., digital ;24 cm. - Pathways in mathematics,2367-3451. - Pathways in mathematics..

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.

ISBN: 9783319335964

Standard No.: 10.1007/978-3-319-33596-4doiSubjects--Topical Terms:

404365
Random walks (Mathematics)

LC Class. No.: QA274.73

Dewey Class. No.: 519.282

The parabolic Anderson model[electronic resource] :random walk in random potential /
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520 $a 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.
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