A necessary and sufficient condition for the -coalescent to come down from the infinity.

Schweinsberg, Jason

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Jan Gustavsson (2001)

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Jamal Najim (2005)

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A Large Deviation Principle (LDP) is proved for the family $\frac{1}{n} \sum_{1}^{n} 𝐟 (x_{i}^{n}) \cdot Z_{i}^{n}$ where the deterministic probability measure $\frac{1}{n} \sum_{1}^{n} δ_{x_{i}^{n}}$ converges weakly to a probability measure $R$ and ${(Z_{i}^{n})}_{i \in ℕ}$ are $ℝ^{d}$ -valued independent random variables whose distribution depends on $x_{i}^{n}$ and satisfies the following exponential moments condition: $sup_{i, n} 𝔼 e^{α^{*} | Z_{i}^{n} |} < + \infty forsome 0 < α^{*} < + \infty .$ In this context, the identification of the rate function is non-trivial due to the absence of equidistribution. We rely on fine convex analysis to address this issue. Among...

Displaying similar documents to “A necessary and sufficient condition for the Λ -coalescent to come down from the infinity.”

Displaying similar documents to “A necessary and sufficient condition for the $Λ$ -coalescent to come down from the infinity.”