Presentacion oral: Ultimate Fate of Constrained Voters

FEDERICO VAZQUEZ

New Brunswick, NJ

Conferencia; 91st Statistical Mechanics Conference (Joel Lebowitz); 2004

Rutgers University

We determine the ultimate fate of a limit of the Axelrod model thatconsists of a population of leftists, centrists, and rightists.  In anelemental interaction between agents, a centrist and a leftist canboth become centrists or both become leftists with equal rates(similarly for a centrist and a rightist), but leftists and rightistsdo not interact.  This interaction is applied repeatedly until thesystem can no longer evolve.  The constraint between extremists canlead to a frustrated final state where the system consists of onlyleftists and rightists.  In the mean field limit, we can view theevolution of the system as the motion of a random walk in the3-dimensional space whose coordinates correspond to the density ofeach species.  We find the exact final state probabilities and thetime to reach consensus by solving for the first-passage probabilityof the random walk to the corresponding absorbing boundaries.  Theextension to a larger number of states will be discussed.  Thisapproach is a first step towards the analytic solution of Axelrod-likemodels.