We study the number of k-cycles in a random graph G（n, p）. We estimate the probability that a random graph contains more k-cycles than expected. In this case, the usual martingale inequality with bounded difference ...We study the number of k-cycles in a random graph G（n, p）. We estimate the probability that a random graph contains more k-cycles than expected. In this case, the usual martingale inequality with bounded difference is not effective. By construct- ing a variable that approximates to the number of k-cycles in a random graph and using a new and extensive martingale inequality, we get the results in this paper.展开更多
We prove some transportation inequalities for hidden Markov chains, generalize the results proved by Kontorovich and Ramanan in two directions and give some applications to log-likelihood functions and hypothesis test...We prove some transportation inequalities for hidden Markov chains, generalize the results proved by Kontorovich and Ramanan in two directions and give some applications to log-likelihood functions and hypothesis testing.展开更多
基金Supported by the National Natural Science Foundation of China (10571139)
文摘We study the number of k-cycles in a random graph G（n, p）. We estimate the probability that a random graph contains more k-cycles than expected. In this case, the usual martingale inequality with bounded difference is not effective. By construct- ing a variable that approximates to the number of k-cycles in a random graph and using a new and extensive martingale inequality, we get the results in this paper.
基金supported by the Youth Innovation Foundation of Zhongnan University of Economics and Law from the Fundamental Research Funds for the Central Universities of China (Grant No. 2009004/31540911202)
文摘We prove some transportation inequalities for hidden Markov chains, generalize the results proved by Kontorovich and Ramanan in two directions and give some applications to log-likelihood functions and hypothesis testing.
