Mathematics – Probability
Scientific paper
2007-06-11
Mathematics
Probability
25 pages. This a substantial revision of an earlier paper. The material has been reorganized, and Theorem 1.3 is new
Scientific paper
Let X^{(k)}(t) = (X_1(t), ..., X_k(t)) denote a k-vector of i.i.d. random variables, each taking the values 1 or 0 with respective probabilities p and 1-p. As a process indexed by non-negative t, $X^{(k)}(t)$ is constructed--following Benjamini, Haggstrom, Peres, and Steif (2003)--so that it is strong Markov with invariant measure ((1-p)\delta_0+p\delta_1)^k. We derive sharp estimates for the probability that ``X_1(t)+...+X_k(t)=k-\ell for some t in F,'' where F \subset [0,1] is nonrandom and compact. We do this in two very different settings: (i) Where \ell is a constant; and (ii) Where \ell=k/2, k is even, and p=q=1/2. We prove that the probability is described by the Kolmogorov capacitance of F for case (i) and Howroyd's 1/2-dimensional box-dimension profiles for case (ii). We also present sample-path consequences, and a connection to capacities that answers a question of Benjamini et. al. (2003)
Khoshnevisan Davar
Levin David A.
Mendez-Hernandez Pedro J.
No associations
LandOfFree
On dynamical bit sequences does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On dynamical bit sequences, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On dynamical bit sequences will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-179782