摘要:随机行走理论已广泛应用与科学研究的许多领域，例如扩散运动,晶格振动,自旋波以及聚合物,化学反应动力学等。上述问题均可以借助于随机行走理论来进行处理。所以，随机行走问题一直被人们所关注。 

　　　本文研究一维复式格子上随机行走——非均匀概率的问题。在这篇文章中，主要的计算方法及计算过程是：首先，掌握并熟练地应用简单一维周期格子上随机行走的主方程方法；其次，将主方程方法运用到一维复式格子上随机行走——非均匀概率的问题中；再次，写出描写演化过程的矩阵，并将描写演化过程的矩阵对角化，在k空间求解演化问题后进行Fourier变换回到坐标空间；最后，求解位移平方的平均。在本论文中,我通过计算及研究，得出i步的随机行走，每一步的平均步长与周期格子间距a有关，而与i取奇数还是偶数和L,S的大小无关。

　　　在本文中，还研究了随机行走和Brown运动的关系。通过研究，我们深刻地知道了随机行走和Brown运动之间有着必然的联系。因此，我们可以用随机行走问题来考察Brown运动。

　　　希望本文研究出的结果能够为解决一维复式格子上随机行走中更复杂的问题奠定一定的基础。

关键词：一维复式晶格；非均匀概率随机行走；主方程方法

Abstract:Random walk theory has been widely applied in many areas of scientific research, such as diffusion, lattice vibrations, spin waves and the polymer, chemical reaction dynamics and so on .Those above issues can be dealt with random walk theory. Therefore, the random walk problem has been of concern to the people.

　　　In this paper, the researcher aimed at studying one-dimensional random walk on lattices - the problem of non-uniform probability. In this article, the main calculation and the calculation process is: Firstly, Understanding and applying the simple one-dimensional periodic lattice random walk master equation; Secondly,Using the equation method to the one-dimensional random walk on lattices—non-uniform probability problems ;Thirdly, writing the matrix describing the evolution, and describing the evolution of the matrix diagonalization, solving the evolution problem in the k space after Fourier transform back to coordinate space; Finally, solving the square displacement average.After the calculation and the study, finding that I step random walk related to each step of the step and cycle the average lattice spacing of a,but not related to i taking odd or even and the size of L,S. 

　　　In this paper, I studied the random walk and the relationship between Brown campaigns. Through research, we are deeply aware of that there is a necessary link between the random walk and Brown exercises. So we can use random walk to examine the Brown campaign issue.

    This research is expected to lay a foundation of solving the one-dimensional lattices the random walk on the more complex issues.

Keywords: One-dimensional lattices；The probability of non-uniform random walk ；Master equation method