In this paper,we study the strong law of large numbers and Shannon-McMillan (S-M) theorem for Markov chains indexed by an infinite tree with uniformly bounded degree.The results generalize the analogous results on a h...In this paper,we study the strong law of large numbers and Shannon-McMillan (S-M) theorem for Markov chains indexed by an infinite tree with uniformly bounded degree.The results generalize the analogous results on a homogeneous tree.展开更多
We consider a branching random walk in random environments, where the particles are reproduced as a branching process with a random environment (in time), and move independently as a random walk on ? with a random env...We consider a branching random walk in random environments, where the particles are reproduced as a branching process with a random environment (in time), and move independently as a random walk on ? with a random environment (in locations). We obtain the asymptotic properties on the position of the rightmost particle at time n, revealing a phase transition phenomenon of the system.展开更多
The probabilities of the state transitions of the initial value S 0 in the S table of RC4 are described by a kind of bistochastic matrices, and then a computational formula for such bistochastic matrices is given, by ...The probabilities of the state transitions of the initial value S 0 in the S table of RC4 are described by a kind of bistochastic matrices, and then a computational formula for such bistochastic matrices is given, by which the mathematical expectation of the number of fixed points in the key extending algorithm of RC4 is obtained. As a result, a statistical weakness of the key extending algorithm of RC4 is presented.展开更多
In this paper,we investigate the expectation of the size of the largest table in an(α,θ)-Chinese restaurant process by using and developing an idea originated in the work by Shepp,which discusses random permutation.
基金the National Natural Science Foundation of China (Grant No.10571076)
文摘In this paper,we study the strong law of large numbers and Shannon-McMillan (S-M) theorem for Markov chains indexed by an infinite tree with uniformly bounded degree.The results generalize the analogous results on a homogeneous tree.
基金the National Natural Science Foundation of China (Grant Nos. 10271020,10471012)SRF for ROCS, SEM (Grant No. [2005]564)
文摘We consider a branching random walk in random environments, where the particles are reproduced as a branching process with a random environment (in time), and move independently as a random walk on ? with a random environment (in locations). We obtain the asymptotic properties on the position of the rightmost particle at time n, revealing a phase transition phenomenon of the system.
基金the National Natural Science Foundation of China (Grant No. 10371061)
文摘The probabilities of the state transitions of the initial value S 0 in the S table of RC4 are described by a kind of bistochastic matrices, and then a computational formula for such bistochastic matrices is given, by which the mathematical expectation of the number of fixed points in the key extending algorithm of RC4 is obtained. As a result, a statistical weakness of the key extending algorithm of RC4 is presented.
基金supported by National Natural Science Foundation of China (Grant No.10671036)the National Basic Research Program of China (Grant No.2007CB814904)
文摘In this paper,we investigate the expectation of the size of the largest table in an(α,θ)-Chinese restaurant process by using and developing an idea originated in the work by Shepp,which discusses random permutation.
