一类随机环境中的高维随机游动

A Class of Multi-dimensional Random Walks in Random Environments

对一类随机环境中的高维(Zd,d≥2)随机游动进行了研究,得出了该模型常返性的一个必要条件:Elogω(x,ei)ω(x,-ei)=0,i=1,…,d。然后在Kalikow0-1律的基础上,讨论了该模型的更新结构,得出了一个对于Xn n的大数定律。

A class of random walks on Z^d,d≥2, in random envrionments is described and analyzed.A necessary condition of recurrence (E logω(x,e-i)ω(x,-e-i)=0,i=1,…,d) is obtained.Using Kalikow's 0-1 law, the renewal structure of the model is discussed and the law of large numbers for X-n/n is derived.