Random walks arise in many models in mathematics and physics and have been used in many fields: ecology, economics, psychology, computer science, physics, chemistry and biology. The goal of this short course is to give a concise introduction to the important ideas in the theory of random walks. We will concentrate on some interesting properties (recurrence, transience and first hitting time, etc.) of random walks.

 

Topics:

I. Markov chains.

II. One–dimensional walks.

III. d-dimensional simple random walk with d>1.

IV. Self-avoiding walk in high dimensions.

 

Reference:

1. F. Spitzer, Principles of Random Walk, Springer- Verlag, 1976.

2. G. F. Lawler. Introduction to Stochastic Process, Chapman & Hall/CRC, 2006.

3. G. Grimmett, Probability and Random Processes, Oxford, 2001.