The parabolic Anderson model and long-range percolation

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The parabolic Anderson model and long-range percolation

Title: The parabolic Anderson model and long-range percolation
Author: Erhard, Dirk
Publisher: Mathematical Institute, Faculty of Science, Leiden University
Issue Date: 2014-07-01
Keywords: Parabolic Anderson equation
Percolation
Quenched Lyapunov exponent
Brownian motion
Abstract: This thesis has two parts. The first part deals with the parabolic Anderson model, which is a stochastic differential equation. It models the evolution of a field of particles performing independent simple random walks with binary branching. The focus of this work is on the exponential growth rate of the solution, where several basic properties are derived. The second part deals with two long-range percolation models. The occupied set of the first model is obtained by taking the union of a collection of independent Brownian motion running up to time t whose initial positions are distributed according to a Poisson Point process. Basic properties such as existence of a percolation phase transition and the uniqueness of the unbounded cluster are proven. The second model is the model of random interlacements. It is shown that the vacant set of random interlacement is transient for almost all values of the supercritical phase as the dimension tends to infinity.
Description: Promotores: W.Th.F.den Hollander, G.Maillard
With Summary in Dutch
Faculty: Faculteit der Wiskunde en Natuurwetenschappen
Citation: Erhard, D., 2014, Doctoral Thesis, Leiden University
Handle: http://hdl.handle.net/1887/26884
 

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application/pdf Title Pages_Contents_Preface 159.4Kb View/Open
application/pdf Part I: Chapter 1 301.1Kb View/Open
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application/pdf Bibliography 157.8Kb View/Open
application/pdf Summary in Dutch 143.4Kb View/Open
application/pdf Acknowledgements_Curriculum Vitae 95.66Kb View/Open
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