Moments of Moments and Branching Random Walks

@article{Bailey2021MomentsOM,
  title={Moments of Moments and Branching Random Walks},
  author={E C Bailey and Jonathan P. Keating},
  journal={Journal of Statistical Physics},
  year={2021},
  volume={182}
}
We calculate, for a branching random walk $$X_n(l)$$ X n ( l ) to a leaf l at depth n on a binary tree, the positive integer moments of the random variable $$\frac{1}{2^{n}}\sum _{l=1}^{2^n}e^{2\beta X_n(l)}$$ 1 2 n ∑ l = 1 2 n e 2 β X n ( l ) , for $$\beta \in {\mathbb {R}}$$ β ∈ R . We obtain explicit formulae for the first few moments for finite n . In the limit $$n\rightarrow \infty $$ n → ∞ , our expression coincides with recent conjectures and results concerning the moments of moments of… 
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