Liouville metric of star-scale invariant fields: tails and Weyl scaling
| Autor: | Dubédat, Julien, Falconet, Hugo |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | We study the Liouville metric associated to an approximation of a log-correlated Gaussian field with short range correlation. We show that below a parameter $\gamma_c >0$, the left-right length of rectangles for the Riemannian metric $e^{\gamma \phi_{0,n}} ds^2$ with various aspect ratio is concentrated with quasi-lognormal tails, that the renormalized metric is tight when $\gamma < \min ( \gamma_c, 0.4)$ and that subsequential limits are consistent with the Weyl scaling. Comment: Final version. To appear in PTRF. 52 pages, 8 figures |
| Databáze: | arXiv |
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