Saakian David B
Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan, Republic of China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jan;85(1 Pt 1):011109. doi: 10.1103/PhysRevE.85.011109. Epub 2012 Jan 4.
We investigate the directed random walk on hierarchic trees. Two cases are investigated: random variables on deterministic trees with a continuous branching, and random variables on the trees constructed through the random branching process. We derive renormalization group (partial differential) equations for the branching models with binomial, Poisson, and compound Poisson distributions of random variables on the links of a tree. These renormalization group equations are a new class of reaction-diffusion equations in one dimension.
我们研究分层树上的有向随机游走。研究了两种情况：具有连续分支的确定性树上的随机变量，以及通过随机分支过程构建的树上的随机变量。我们推导了树的链上具有二项式、泊松和复合泊松分布的随机变量的分支模型的重整化群（偏微分）方程。这些重整化群方程是一类新的一维反应扩散方程。
