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- W2000452923 abstract "We study the asymptotics of a Markovian system of N ≥ 3 particles in [0, 1] d in which, at each step in discrete time, the particle farthest from the current centre of mass is removed and replaced by an independent U [0, 1] d random particle. We show that the limiting configuration contains N − 1 coincident particles at a random location ξ N ∈ [0, 1] d . A key tool in the analysis is a Lyapunov function based on the squared radius of gyration (sum of squared distances) of the points. For d = 1, we give additional results on the distribution of the limit ξ N , showing, among other things, that it gives positive probability to any nonempty interval subset of [0, 1], and giving a reasonably explicit description in the smallest nontrivial case, N = 3." @default.
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- W2000452923 date "2015-03-01" @default.
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- W2000452923 title "Convergence in a Multidimensional Randomized Keynesian Beauty Contest" @default.
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