Two particles’ repelling random walks on the complete graph. (English) Zbl 1307.60048

Chen, Jun

Electron. J. Probab. 19, Paper No. 113, 17 p. (2014).

Summary: We consider two particles’ repelling random walks on complete graphs. In this model, each particle has higher probability to visit the vertices which have been seldom visited by the other one. By a dynamical approach we prove that the two particles’ occupation measure asymptotically has small joint support almost surely if the repulsion is strong enough.

MSC:

60G50	Sums of independent random variables; random walks
60K35	Interacting random processes; statistical mechanics type models; percolation theory
05C81	Random walks on graphs
37C10	Dynamics induced by flows and semiflows

Keywords:

repelling random walks; reinforced random walk; complete graph; chain recurrent set; Lyapunov function