Mathematical Sciences: Studies in Lattice Random Walks

点击翻译按钮获取中文摘要

The investigator will study two problems dealing with random walks. The first problem of self avoiding random walks has applications in chemical physics as a model for polymer chains. The properties of self avoiding walks will be analyzed via the mathematically more tractable intersection properties of two simple random walks. The second problem of the random walks in random environments has applications in many fields including biology and chemistry. The general problem of the field is to find properties of a markov chain when its transition matrix is chosen from some probability distribution. The investigator has had a strong record in both areas already and has exiting new ideas for the new problems proposed.