Moments of moments and branching random walks

Author: 

Bailey, E
Keating, J

Publication Date: 

12 January 2021

Journal: 

Journal of Statistical Physics

Last Updated: 

2021-10-11T19:31:44.983+01:00

Issue: 

2021

Volume: 

182

DOI: 

10.1007/s10955-020-02696-9

abstract: 

We calculate, for a branching random walk Xn(l) to a leaf l at depth n on a binary tree, the positive integer moments of the random variable 12n∑2nl=1e2βXn(l), for β∈R. We obtain explicit formulae for the first few moments for finite n. In the limit n→∞, our expression coincides with recent conjectures and results concerning the moments of moments of characteristic polynomials of random unitary matrices, supporting the idea that these two problems, which both fall into the class of logarithmically correlated Gaussian random fields, are related to each other.

Symplectic id: 

1151211

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article