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The asymptotic distribution of the length of Beta-coalescent trees
Beta-coalescent coupling, point process stable distribution Probability
2011/9/6
Abstract: We derive the asymptotic distribution of the total length $L_n$ of a Beta($2-\alpha,\alpha$)-coalescent tree for $1<\alpha < 2$, starting from $n$ individuals. There are two regimes: If $\al...
Asymptotic expansion of beta matrix models in the one-cut regime
Asymptotic expansion beta matrix models the one-cut regime Probability
2011/8/26
Abstract: We prove the existence of a 1/N expansion to all orders in beta matrix models with a confining, off-critical potential corresponding to an equilibrium measure with a connected support. Thus,...