2025/11/18 by Hartung, Lisa, Klippel, Andreas, Mönch, Christian
Mathematics · Economics, Econometrics and Finance · #Stochastic processes and statistical mechanics #Random Matrices and Applications #Financial Risk and Volatility Modeling
paper · doi:10.48550/arxiv.2511.14026
We study the extreme value statistics of the zero-average Gaussian free field (GFF) on random r-regular graphs and the Gaussian free field on r-regular trees. For random r-regular graphs of diverging size, for every fixed r≥3, we show that the rescaled extremal point process of the field is asymptotically distributed, in the annealed sense, as a Poisson point process on the line with intensity e-x dx. The same limit behaviour is obeyed by the restriction of the GFF on r-regular trees to finite subsets of vertices. Our approach relies on a direct Gaussian comparison argument and precise Green function estimates.