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Article overview
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Normal approximation for Gibbs processes via disagreement couplings | | Christian Hirsch
; Moritz Otto
; Anne Marie Svane
; | | Date: |
1 Sep 2023 | | Abstract: | This work improves the existing central limit theorems (CLTs) on Gibbs
processes in three aspects. First, we derive a CLT for weakly stabilizing
functionals, thereby improving on the previously used assumption of exponential
stabilization. Second, we show that this CLT holds for interaction ranges up to
the percolation threshold of the dominating Poisson process. This avoids
imprecise branching bounds from graphical construction. Third, by extending the
concept of Stein couplings from the Poisson to the Gibbs setting, we provide a
quantitative CLT in terms of Kolmogorov bounds for normal approximation. An
important conceptual ingredient in these advances are extensions of
disagreement coupling adapted to increasing windows and to the comparison at
multiple spatial locations. | | Source: | arXiv, 2309.00394 | | Services: | Forum | Review | PDF | Favorites | |
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