Mathematical Sciences: Studies in Lattice Random Walks

研究者将研究两个问题， 走路. 自避免随机游动的第一个问题是 在化学物理学中作为聚合物链模型的应用。 自避行走的性质将通过 数学上更易处理的两个 简单的随机漫步 中随机游动的第二个问题 随机环境在许多领域都有应用，包括 生物学和化学。 该领域的一般问题是， 求马尔可夫链的转移矩阵为 从某种概率分布中选出。 研究者已 在这两个领域都有很好的记录， 提出了新问题的思路。

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.