Sunday, 29 November 2009

An unintuitive probability problem

Probability can do strange things to your mind. This week I had a probability problem where every time I tried to use intuition to solve it I ended up going completely wrong. I thought I'd share it as I think it's interesting.

Consider a one dimensional random walk. At each time step my walker will go left with probability , and right with probability . It stays where it is with probability . Furthermore these probabilities are dependent on the walker's position in space, so it's really and . I'm imagining I'm on a finite line of length, L, although it doesn't matter too much.

Now if , then we just have a normal random walker. In my problem I have the following setup: but . What does this mean? At any given point, x, my walker is more likely to go left than right. If it does go left it will come back with the same rate (although it's more likely to go left again).

So here's the question: If I leave this for a really long time, what is the equilibrium probability distribution for the walkers position, ?

Friday, 20 November 2009

Great LHC animation

The purpose of this blog was to showcase other types of physics other than the LHC. But I can't resist, this is a really nice animated video showing the stages of getting stationary protons up to 7TeV

(via @CERN)