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• W2954928958 abstract "In a recent series of works, Miller and Sheffield constructed a metric on $sqrt{8/3}$-Liouville quantum gravity (LQG) under which $sqrt{8/3}$-LQG surfaces (e.g., the LQG sphere, wedge, cone, and disk) are isometric to their Brownian surface counterparts (e.g., the Brownian map, half-plane, plane, and disk). We identify the metric gluings of certain collections of independent $sqrt{8/3}$-LQG surfaces with boundaries identified together according to LQG length along their boundaries. Our results imply in particular that the metric gluing of two independent instances of the Brownian half-plane along their positive boundaries is isometric to a certain LQG wedge decorated by an independent chordal SLE$_{8/3}$ curve. If one identifies the two sides of the boundary of a single Brownian half-plane, one obtains a certain LQG cone decorated by an independent whole-plane SLE$_{8/3}$. If one identifies the entire boundaries of two Brownian half-planes, one obtains a different LQG cone and the interface between them is a two-sided variant of whole-plane SLE$_{8/3}$. Combined with another work of the authors, the present work identifies the scaling limit of self-avoiding walk on random quadrangulations with SLE$_{8/3}$ on $sqrt{8/3}$-LQG." @default.
• W2954928958 created "2019-07-12" @default.
• W2954928958 creator A5019995974 @default.
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• W2954928958 date "2016-08-02" @default.
• W2954928958 modified "2023-10-01" @default.
• W2954928958 title "Metric gluing of Brownian and $sqrt{8/3}$-Liouville quantum gravity surfaces" @default.
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