2020/02/03 by Maximilian Fels, Fels, Maximilian, Lisa Hartung +1
Economics, Econometrics and Finance · Mathematics · #60G15 #60G60 #60G70 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2002.00925
openalex publication_date 2020/02/03 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We prove convergence of the full extremal process of the two-dimensional\nscale-inhomogeneous discrete Gaussian free field in the weak correlation\nregime. The scale-inhomogeneous discrete Gaussian free field is obtained from\nthe 2d discrete Gaussian free field by modifying the variance through a\nfunction \I:[0,1]\→ [0,1]. The limiting process is a\ncluster Cox process. The random intensity of the Cox process depends on the\n\I^\′(0) through a random measure Y and on the\n\I^\′(1) through a constant \β. We describe the cluster\nprocess, which only depends on \I^\′(1), as points of a standard\n2d discrete Gaussian free field conditioned to be unusually high.\n