## DescriptionRandom walks are basic models of dynamics subject to random fluctuations, with wide-ranging applications in, for instance, physics
(Brownian motion), finance (market models), and biology (microbe locomotion). In simple symmetric random walk on
the A celebrated theorem of Polya says that the walk will return to its starting point again and again when The project will involve investigating aspects of random walks (with scope for simulation), including the connection to the theory of electrical networks, and applications, for example, to gambling problems. There will also be scope for simulation. ## Prerequisites2H Probability is essential. 3H Stochastic Processes is strongly recommended. Students taking the 4H Probability course may find it helpful, but it is not essential for the project. If you can remember a little basic electrical network theory from school physics, that will help! ## ResourcesFor some background on what may be involved, you should: - revise material on random walks and Markov chains from previous courses;
- look at some of the recommended literature (or other literature you find) to see which look most helpful; look at resources e.g. on the web;
- read the introductory material in Doyle and Snell, and look at Chapters 3 and 14 of Feller (see below).
- Random walks and electric networks, P.G. Doyle and J.L. Snell, 2000. Available here.
- Introduction to Probability Theory and Its Applications, Volume I, W. Feller, 3rd ed., 1968. Chapters 3 and 14 for random walks and gambler's ruin; also Chapters 15 and 16 are relevant.
- Probability and Random Processes, G. Grimmett and D. Stirzaker, 3rd ed., 2001.
- Lectures on Contemporary Probability, G.F. Lawler and L.N. Coyle, 1999. Chapters 1 and 2 give a streamlined discussion of simple random walk.
- Problems and Snapshots from the World of Probability, G. Blom, L. Holst, and D. Sandell, 1994. Chapter 10.
Get in touch if you would be interested in probability, doing some simulations and/or have any questions! |

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email:
Chak Hei Lo,
Andrew Wade
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