Project: Random Walk


This handout contains the information you need to get going on your project. There are two parts to the handout. This first part has information about due dates for the project, the report you will be preparing, grading criteria, and a list of students doing the project to help you in forming a group if you choose to do so. The second part has a brief summary of your topic and a list of key words to help you head in the right direction. In the next two weeks you will get one more handout which will contain problems for you to solve as part of your project.

The material I'm giving you really is just a bare-bones minimum to help direct you. You are responsible for finding references and doing your own investigating and learning. However please feel free to contact me, in person or by email, for help finding references or working the problems or for general guidance about the projects, and to give me feedback about how it is going.

Due Dates

There are two due dates for the project: October 30th, November 22nd. On October 30th, you should turn in:

1. At least two references which you have found for your project.

2. An explanation or definition of at least two of the key words for your topic.

Turning this material in on time will count towards points in the determination of your total grade on the project.


On Wednesday, November 22nd your overall project report is due.

Each person will be responsible for preparing his/her own report, including writing up his/her own solutions to the problems.

Reports and Grading Criteria
Your report should include some version of the following 5 parts. They do not have to be arranged the way I list them here, but all should be included in your report in some form or another.

  1. (10 points) General Discussion Introduction and generalities for the project (could include why you chose this project, background about the field of application, goals of the project), definitions and results from Probability used in the project, definitions and discussion of results you use, try to explain some of the mathematics behind why the results are true-present a derivation if you can, or, if that is too difficult, give a sketch or an intuitive idea of how it works.

  2. (25 points) Solutions to Problems Give your solutions to the problems I will provide for your topic. It is very important not only to give a correct answer but also to give a thorough explanation of your solution. You should have a clear explanation of each step, an analysis of what results apply to what step, etc. This is not like just working out a usual homework problem-explain in words what you are doing and write sentences.

  3. (6 points) References A list of the references that you used, people you consulted, people you worked with, places you found help. Included in the 6 points will be turning in on time your two references and key words on October 30th as mentioned above.

  4. (2 points) Comments Your comments on how interesting you found the project, whether you feel that the time you spent on this was worthwhile and whether it might help you in the future or lead to anything for you, and suggestions to me for improvements in case I do projects like this again.

  5. (7 points) Presentation This includes innovation in presenting the material of the report, clarity and neatness, flow, design and organization of the report, and creativity used in explaining the ideas.

Project Details

Suppose you start at the street corner nearest to your house. You pick a side with equal probability and walk along that side. When you arrive at the next street corner you pick a side with equal probability and walk along till the next street corner. This process is called a Simple Random walk.

In this project we shall set up a sample space and a random variable to work with. This random variable will indicate your position at the nth step. We shall also study some properties of this process. For instance, will we ever return (with probability one) to our starting point ?.

Key words to Learn :

  1. Simple Random walk
  2. Symmetric Random walk.
  3. Sums of independent random variables.
  4. Markov chain or Markov process.
  5. Time Reversible.
  6. Recurrence.
  7. Transience.

http://www.math.ubc.ca/~athreya/302/projects/randomwalk.html
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