62 citations · 338 across the 22 of their papers we have counts for
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math.PR2004★ 62 cited
Vertex-reinforced random walk on Z eventually gets stuck on five points
Pierre Tarres
Vertex-reinforced random walk (VRRW), defined by Pemantle in 1988, is a random process that takes values in the vertex set of a graph G, which is more likely to visit vertices it h…
math.PR2004★ 37 cited
Generalized Urn Models of Evolutionary Processes
Michel Benaim, Sebastian J. Schreiber, Pierre Tarres
Generalized Polya urn models can describe the dynamics of finite populations of interacting genotypes. Three basic questions these models can address are: Under what conditions doe…
math.PR2004★ 32 cited
When can the two-armed bandit algorithm be trusted?
Damien Lamberton, Gilles Pages, Pierre Tarres
We investigate the asymptotic behavior of one version of the so-called two-armed bandit algorithm. It is an example of stochastic approximation procedure whose associated ODE has b…