Let be the simple random walk in zd, and SupPers f(n) is an integer-valued function and increases to infinity as n tends to infinity, and In this paper,a necessary and sufficient condition to ensure or 1 is derived fo...Let be the simple random walk in zd, and SupPers f(n) is an integer-valued function and increases to infinity as n tends to infinity, and In this paper,a necessary and sufficient condition to ensure or 1 is derived for d=3,4. This problem was first studied by P. Erdos and S.J. Taylor.展开更多
The range of random walk on Z￣d in symmetric random environment is investigated. As results, it is proved that the strong law of large numbers for the range of random walk on Zdin some random environments holds if d...The range of random walk on Z￣d in symmetric random environment is investigated. As results, it is proved that the strong law of large numbers for the range of random walk on Zdin some random environments holds if d≥ 3, and a weak law of large numbers holds for d= 1.展开更多
文摘Let be the simple random walk in zd, and SupPers f(n) is an integer-valued function and increases to infinity as n tends to infinity, and In this paper,a necessary and sufficient condition to ensure or 1 is derived for d=3,4. This problem was first studied by P. Erdos and S.J. Taylor.
文摘The range of random walk on Z￣d in symmetric random environment is investigated. As results, it is proved that the strong law of large numbers for the range of random walk on Zdin some random environments holds if d≥ 3, and a weak law of large numbers holds for d= 1.
