So, you thought I couldn’t handle writing a whopping two blog posts in one month,
well HAHA, my non-existent audience. Here it is, Blogging My Class Issue 2: The homework strikes back! So, this weeks topic is the drunken walk, and how we can use it for good, rather than evil.
Drunken (Random) Walks
So, picture this: you are a drunk, zero dimensional particle sitting on a one dimensional line of integers (since you have zero volume, an infinitesimal volume of booze is needed to get you drunk). The non-existent alcohol sloshing around in your non-existent veins causes you to become extremely indecisive, and when you decide to jump to a point adjacent to the one you stand on, you will randomly jump either left or right. In the simplest example, you will choose left or right equally often. Since you a sloshed singularity, you forget where you are going after each jump, and so for each jump, you choose left or right again randomly. This is the discrete random walk. For the simple example, you will likely move left approximately as often as you move right, and thus end up right back where you started! Now, you can simply expand your one-dimensional space from integers to real numbers, and now take steps of different size as well to get a continuous random walk, but the basic idea is the same. This simple model is cool, because you can use it for tons of different things. In statistical mechanics, it is used as a model for the motion of a particle in a gas as it bounces off of other particles and the walls (just represent each dimension of motion as a continuous drunken walk). It can be expanded to include a quantum drunk (who moves both left and right simultaneously!) to create quantum computer elements (like quantum logic gates). It’s even been used to estimate the size of the Web. Nifty.