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The simplest version of percolation takes place on , which we view as a graph with edges between neighbouring vertices. All edges of are, independently of each other, chosen to be open with probability and closed with probability. Clearly and , since there are no open edges at all when and all edges are open when.


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For some models there is a such that the global behaviour of the system is quite different for and for. Such a sharp transition in global behaviour of a system at some parameter value is called a phase transition or a critical phenomenon, and the parameter value at which the transition takes place is called a critical value.

(1) Overview

The basic mathematical methods and techniques of random processes and an overview of the most important applications will enable the student to use analytical techniques and models to study questions in modern applications in biological and physical systems, communication networks, financial market, decision processes.

Georgii: Stochastics: introduction to probability theory and statistics , de Gruyter Norris: Markov chains , Cambridge University Press [standard reference treating the topic with mathematical rigor and clarity, and emphasizing numerous applications to a wide range of subjects].

Grimmett, D. Riordan: Percolation , Cambridge University Press The introduction and the chapter on basic techniques are relevant for the lecture]. Grimmett: Percolation , 2nd ed. It contains much more than covered in the lecture. The first two chapters are relevant for the lecture].

Markov Chains - Part 1

Archived Pages: Year 3 regs and modules G G Year 4 regs and modules G Download preview PDF. Skip to main content. Advertisement Hide. On the functional central limit theorem and the law of the iterated logarithm for Markov processes. Authors Authors and affiliations R. This process is experimental and the keywords may be updated as the learning algorithm improves.

Inversion of Markov processes to determine rate constants from single-channel data.

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MA3H2 Markov Processes and Percolation Theory

Bhattacharya, R. Google Scholar. Correction Note, Ibid, 8 , —95 Google Scholar. Bhattacharaya, R. Multivariate Analysis. To appear: Google Scholar. Billingsley, P. New York: Wiley Google Scholar. Blumenthal, R. New York: Acad.

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