Branching random walk with exponentially decreasing steps, and stochastically self-similar measures

Details Branching random walk with exponentially decreasing steps, and stochastically self-similar measures Branching random walk with exponentially decreasing steps, and stochastically self-similar measures

2006-08-10

arxiv.org/abs/math/0608271v2

Trans. Amer. Math. Soc. 361 (2009), no. 3, 1625--1643

Mathematics

Probability

Minor corrections after the referee report and a remark added at the end. To appear in Transactions of the AMS

Scientific paper

We consider a Branching Random Walk on $\R$ whose step size decreases by a fixed factor, $01/2$ the limit measure is almost surely (a.s.) absolutely continuous with respect to the Lebesgue measure, but for Pisot $1/b$ it is a.s. singular; (2) for all $b > (\sqrt{5}-1)/2$ the support of the measure is a.s. the closure of its interior; (3) for Pisot $1/b$ the support of the measure is ``fractured'': it is a.s. disconnected and the components of the complement are not isolated on both sides.

Affiliated with

Also associated with

No associations

Rating

Branching random walk with exponentially decreasing steps, and stochastically self-similar measures 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 Branching random walk with exponentially decreasing steps, and stochastically self-similar measures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Branching random walk with exponentially decreasing steps, and stochastically self-similar measures will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-547531