A Class of Multi-particle Reinforced Interacting Random Walks

2012/10/14 by Jun Chen, Chen, Jun
Computer Science · Decision Sciences · Mathematics · #Advanced Multi-Objective Optimization Algorithms #Simulation Techniques and Applications #Stochastic processes and statistical mechanics #math.DS #math.PR

paper · pdf · doi:10.48550/arxiv.1210.3795

19 pages

arxiv created 2013/03/23 · arxiv updated 2013/03/26

Abstract

We consider a class of multi-particle reinforced interacting random walks. In this model, there are some (finite or infinite) particles performing random walks on a given (finite or infinite) connected graph, so that each particle has higher probability to visit neighboring vertices or edges which have been seldom visited by the other particles. Specifically we investigate two particles' vertex-reinforced interacting random walks on finite complete graphs. By a dynamical approach we prove that the two particles' occupation measure asymptotically has small joint support almost surely if the reinforcement is strong.

Citations

• A Stochastic Approximation Method
• Stochastic Estimation of the Maximum of a Regression Function

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