Gathering of Agents on the Line

Dmitry Rabinovich, M.Sc. Thesis Seminar
Wednesday, 26.7.2017, 14:30
Taub 601
Prof. A.M.Bruckstein

We consider a group of mobile agents on a line, identical and indistinguishable, memoryless, having the capability to only sense the presence of neighboring agents to the left and to the right. The agents' rule of motion is as follows : at each moment, agents with neighbors on both sides stay put, while agents with neighbors on one side only jump with high probability a unit distance towards the neighbors (otherwise, they jump one unit away). We prove that all agents, except two, gather almost surely inside a unit size interval in finite expected time. Two agents, the current left-most and right-most ones perform random walks strongly biased towards the cluster of other agents. The cluster of gathered agents slowly moves on the line. Interesting interactions occur when the left and/or right Random Walkers reach the clustered agents and these interactions are completely analyzed herein.

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