Consistent Minimal Displacement of Branching Random Walks
Dublin Core | PKP Metadata Items | Metadata for this Document | |
1. | Title | Title of document | Consistent Minimal Displacement of Branching Random Walks |
2. | Creator | Author's name, affiliation, country | Ming Fang; University of Minnesota |
2. | Creator | Author's name, affiliation, country | Ofer Zeitouni; University of Minnesota and Weizmann Institute |
3. | Subject | Discipline(s) | |
3. | Subject | Keyword(s) | Branching Random Walk; Consistent Minimal Displacement |
3. | Subject | Subject classification | 60G50; 60J80 |
4. | Description | Abstract | Let $\mathbb{T}$ denote a rooted $b$-ary tree and let $\{S_v\}_{v\in \mathbb{T}}$ denote a branching random walk indexed by the vertices of the tree, where the increments are i.i.d. and possess a logarithmic moment generating function $\Lambda(\cdot)$. Let $m_n$ denote the minimum of the variables $S_v$ over all vertices at the $n$th generation, denoted by $\mathbb{D}_n$. Under mild conditions, $m_n/n$ converges almost surely to a constant, which for convenience may be taken to be $0$. With $\bar S_v=\max\{S_w: w$ is on the geodesic connecting the root to $v \}$, define $L_n=\min_{v\in \mathbb{D}_n} \bar S_v$. We prove that $L_n/n^{1/3}$ converges almost surely to an explicit constant $l_0$. This answers a question of Hu and Shi. |
5. | Publisher | Organizing agency, location | |
6. | Contributor | Sponsor(s) | NSF; Weizmann |
7. | Date | (YYYY-MM-DD) | 2010-03-29 |
8. | Type | Status & genre | Peer-reviewed Article |
8. | Type | Type | |
9. | Format | File format | |
10. | Identifier | Uniform Resource Identifier | http://ecp.ejpecp.org/article/view/1533 |
10. | Identifier | Digital Object Identifier | 10.1214/ECP.v15-1533 |
11. | Source | Journal/conference title; vol., no. (year) | Electronic Communications in Probability; Vol 15 |
12. | Language | English=en | |
14. | Coverage | Geo-spatial location, chronological period, research sample (gender, age, etc.) | |
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