Branching random walk and probability problems from physics and biology

• Main Author: Johnson, Torrey (Torrey Allen)
• Other Authors: Waymire, Edward C.
• Language: en_US
• Published: 2012
• Subjects: tree polymer; disorder; branching random walk; critical; site-selection; ecology; Random walks (Mathematics); Bees > Swarming > Mathematical models
• Online Access: http://hdl.handle.net/1957/30268

This thesis studies connections between disorder type in tree polymers and the branching random walk and presents an application to swarm site-selection. Chapter two extends results on tree polymers in the infinite volume limit to critical strong disorder. Almost sure (a.s.) convergence in the infinite volume limit is obtained for weak disorder by standard theory on multiplicative cascades or the branching random walk. Chapter three establishes results for a simple branching random walk in connection with a related tree polymer. A central limit theorem (CLT) is shown to hold regardless of polymer disorder type, and a.s. connectivity of the support is established in the asymmetric case. Chapter four contains a model for site-selection in honeybee swarms. Simulations demonstrate a trade-off between speed and accuracy, and strongly suggest that increasing the quorum threshold at which the process terminates usually improves decision performance. === Graduation date: 2013