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• W2485791703 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 $mathrm{SLE}_{8/3}$ 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 $mathrm{SLE}_{8/3}$. 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 $mathrm{SLE}_{8/3}$. Combined with another work of the authors, the present work identifies the scaling limit of self-avoiding walk on random quadrangulations with $mathrm{SLE}_{8/3}$ on $sqrt{8/3}$-LQG." @default.
• W2485791703 created "2016-08-23" @default.
• W2485791703 creator A5019995974 @default.
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• W2485791703 date "2019-07-01" @default.
• W2485791703 modified "2023-09-26" @default.
• W2485791703 title "Metric gluing of Brownian and $sqrt{8/3}$-Liouville quantum gravity surfaces" @default.
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• W2485791703 doi "https://doi.org/10.1214/18-aop1309" @default.
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