Chung-Diaconis-Graham随机过程的一个下界
A lower bound for the Chung-Diaconis-Graham random process
摘要：
Chung，Diaconis和Graham考虑了随机过程的形式X_{n+1} =a_n X_n+b_n（mod p）其中p是奇数，X_0=0，a_n总是=2，b_n是独立同分布的。对于n= 0，1，2，. .本文证明了：若P（b_n=-1）=P（b_n=0）=P（b_n=1）=1/3，则存在一个常数c>1，使得clog_2p步不足以使X_n在模p的整数上接近均匀分布.
英文摘要：
Chung, Diaconis, and Graham considered random processes of the form X_{n+1}=a_n X_n+b_n (mod p) where p is odd, X_0=0, a_n=2 always, and b_n are i.i.d. for n=0,1,2,... . In this paper, we show that if P(b_n=-1)=P{b_n=0)=P(b_n=1)=1/3, then there exists a constant c>1 such that c log_2 p steps are not enough to make X_n get close to uniformly distributed on the integers mod p.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
