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Random walks and the contact process
This thesis concerns the mathematical analysis of certain random walks in a dynamic random environment. Such models are important in the understanding of various models in physics, chemistry and biology. The interest is in questions such as how to determine the average velocity of the random walker and how to control fluctuations and deviations thereof. This is in general a very challenging problem due to the possibility of strong dependence both in space and time, and many problems are still wide open.
After a general introduction in Chapter 1, we present several approaches for determining the asymptotic behaviour for random walks in a dynamic random environment in Chapter 2-5 of this thesis. Our work improves on the existing literature for general models with strongly mixing dynamics and provides new insight for certain models with poorly mixing dynamics. One particular model is analysed in more detailed, namely the so-called contact process. This model is a...
Show moreThis thesis concerns the mathematical analysis of certain random walks in a dynamic random environment. Such models are important in the understanding of various models in physics, chemistry and biology. The interest is in questions such as how to determine the average velocity of the random walker and how to control fluctuations and deviations thereof. This is in general a very challenging problem due to the possibility of strong dependence both in space and time, and many problems are still wide open.
After a general introduction in Chapter 1, we present several approaches for determining the asymptotic behaviour for random walks in a dynamic random environment in Chapter 2-5 of this thesis. Our work improves on the existing literature for general models with strongly mixing dynamics and provides new insight for certain models with poorly mixing dynamics. One particular model is analysed in more detailed, namely the so-called contact process. This model is a prototype of a dynamic random environment with poor mixing properties. In addition to results for certain random walks with the contact process as dynamic random environment, we also provide new insight for the contact process itself, given in Chapter 5.
Show less- All authors
- Bethuelsen, S.A.
- Supervisor
- Hollander, W.T.F. den; Heydenreich, M.O.
- Committee
- Stevenhagen, P.; Mountford, T.; Birkner, M.; Valesin, D.
- Qualification
- Doctor (dr.)
- Awarding Institution
- Institute of Mathematics , Science , Leiden University
- Date
- 2016-11-22
Funding
- Sponsorship
- The research documented in this thesis is supported by the Netherlands Organisation for Scientific Research (NWO) through Mathematics cluster STAR.