On Self-Avoiding Walks

Today I came across an interesting question on the mathoverflow: what are the biggest problems in probability theory? In the answers, there is one about self-avoiding walks. And the most famous scientist in this field, as far as I know, is Gordon Slade. And several days ago, I also saw a post of this subject. At that time, I have no idea about this area, so I did not have anything feeling about this and then I just skipped it. Now I think I have realized the importance of this field in the whole probability theory. Thus I have to know something about this, at least getting to know what it is. Here I want to share you with the materials I have collected.

http://chromotopy.org/?p=402 (a recent post about the talk given by Professor Slade)

http://gowers.wordpress.com/2010/08/22/icm2010-smirnov-laudatio/ (a post about this area)

http://terrytao.wordpress.com/2010/08/19/lindenstrauss-ngo-smirnov-villani/ (a post about the winners in icm2010, including this area)

Free Probability

I have noticed this concept before. Since I am just new in Probability field, so you should forgive me that I just noticed this academic area several months ago and did not realize the importance of it. Today I attended the regular colloquium of my department and the speaker, Zbigniew J. Jurek, gave a lecture about The Random Integral Representation Conjecture. In this talk, he mentioned free probability. Moreover, he also joked that free statistics will come into being.

I also fount a useful link about the survey of free probability. I hope it will be useful for you. Terry Tao also have a post about this.