Mathematical Sciences: Studies in Lattice Random Walks

研究人员将研究两个与随机行走有关的问题。自避免随机游动的第一个问题作为高分子链的模型在化学物理中得到了应用。将通过两个简单随机行走的数学上更容易处理的相交性质来分析自回避行走的性质。第二个问题是随机环境中的随机游动问题，它在生物、化学等领域有着广泛的应用。该领域的一般问题是当马尔可夫链的转移矩阵从某种概率分布中选取时，寻找它的性质。这位研究人员已经在这两个领域都有了很好的记录，并对提出的新问题提出了新的想法。

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.