Maury Bramson and Ofer Zeitouni J. Stat. Mech. (2007) P07010 doi:10.1088/1742-5468/2007/07/P07010
Tightness for the minimal displacement of branching random walk
FREE ARTICLE Focus on Dynamics of Non-Equilibrium SystemsMaury Bramson1 and Ofer Zeitouni1,2,3
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Recursion equations have been used to establish weak laws of large numbers for the minimal displacement of branching random walk in one dimension. Here, we use these equations to establish the tightness of the corresponding sequences after appropriate centering. These equations are special cases of recursion equations that arise naturally in the study of random variables on tree-like structures. Such recursion equations are investigated in detail, in Bramson and Zeitouni (2006 Preprint math.PR/0612382v1), in a general context. Here, we restrict ourselves to investigating the more concrete setting of branching random walk, and provide motivation for the rigorous arguments that are given in Bramson and Zeitouni. We also discuss briefly the cover time of symmetric simple random walk on regular binary trees, which is another application of the more general recursion equations.
- Keywords
- PACS
- MSC
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82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
- Subjects
- Dates
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Issue 07 (July 2007)
Received 13 February 2007, accepted for publication 25 April 2007
Published 6 July 2007
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Tightness for the minimal displacement of branching random walk
Maury Bramson and Ofer Zeitouni J. Stat. Mech. (2007) P07010
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