What Are the Key Concepts of Random Walks for a Grade 12 Project?

[robyn]

Hey there. Right now, I am doing a project for my grade 12 Geometry and Discrete class on any topic of our choosing. I have chosen the subject of RANDOM WALKS, and I am looking for any information on this subject at all, as I seemed to have hit a plateau of information, where all of my new information just seems to be repeating other resourses. The point of the project is to write a paper on the subject, and its uses. I am really open to any help or assistance on the topic at all, anything will be of help. Thanks!

 

[Tide]

How about exploring the fact that in either 1- or 2-D random walks you are always guaranteed to eventually return to your starting point whereas it is not certain in 3-D?

 

[robyn]

That is actually quite a good idea, i never thought of that yet. That could be a good approach, i was also thinking of incorporating the stock market and how that relates too, but I'm not sure if that is pulling too far away from the topic or not.

 

[shmoe]

Explaining exactly what is meant by "..guaranteed to eventually return to your starting point.." would be a worthy related topic. If you like number theory, you might compare Merten's function with random walks.