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- Title
Extremes of the 2d scale-inhomogeneous discrete Gaussian free field: Extremal process in the weakly correlated regime.
- Authors
Fels, Maximilian; Hartung, Lisa
- Abstract
We prove convergence of the full extremal process of the two-dimensional scale-inhomogeneous discrete Gaussian free field in the weak correlation regime. The scale-inhomogeneous discrete Gaussian free field is obtained from the 2d discrete Gaussian free field by modifying the variance through a function I:[0,1]→[0,1]. The limiting process is a cluster Cox process. The random intensity of the Cox process depends on the I'(0) through a random measure Y and on the I'(1) through a constant β. We describe the cluster process, which only depends on I'(1), as points of a standard 2d discrete Gaussian free field conditioned to be unusually high.
- Subjects
STOCHASTIC convergence; GAUSSIAN function; EXTREMAL problems (Mathematics); BROWNIAN motion; BRANCHING processes
- Publication
ALEA. Latin American Journal of Probability & Mathematical Statistics, 2021, Vol 18, p1689
- ISSN
1980-0436
- Publication type
Article
- DOI
10.30757/ALEA.v18-62