# Unit boundary length quantum disk: a study of two different perspectives and their equivalence

@article{Cercle2019UnitBL, title={Unit boundary length quantum disk: a study of two different perspectives and their equivalence}, author={Baptiste Cercl'e}, journal={arXiv: Probability}, year={2019} }

The theory of the 2-dimensional Liouville Quantum Gravity, first introduced by Polyakov in his 1981 work has become a key notion in the study of random surfaces. In a series of articles, David, Huang, Kupiainen, Rhodes and Vargas, on the one hand, and Duplantier, Miller and Sheffield on the other hand, investigated this topic in the realm of probability theory, and both provided definitions for fundamentals objects of the theory: the unit area quantum sphere and the unit boundary length quantum…

## 10 Citations

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For $\gamma \in (0,2)$, the quantum disk and $\gamma$-quantum wedge are two of the most natural types of Liouville quantum gravity (LQG) surfaces with boundary. These surfaces arise as scaling limits…

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. We obtain exact formulae for three basic quantities in random conformal geometry that depend on the modulus of an annulus. The ﬁrst is for the law of the modulus of the Brownian annulus describing…

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Liouville theory is a fundamental example of a conformal field theory (CFT) first introduced by Polyakov in the context of string theory. Conformal blocks are objects underlying the integrable…

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We show that when one draws a simple conformal loop ensemble (CLE$_\kappa$ for $\kappa \in (8/3,4)$) on an independent $\sqrt{\kappa}$-Liouville quantum gravity (LQG) surface and explores the CLE in…

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We demonstrate that the conformal loop ensemble (CLE) has a rich integrable structure by establishing exact formulas for two CLE observables. The first describes the joint moments of the conformal…

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We demonstrate how to obtain integrability results for the Schramm-Loewner evolution (SLE) from Liouville conformal field theory (LCFT) and the mating-of-trees framework for Liouville quantum gravity…

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We show that for each $$\gamma \in (0,2)$$ γ ∈ ( 0 , 2 ) , there is a unique metric (i.e., distance function) associated with $$\gamma $$ γ -Liouville quantum gravity (LQG). More precisely, we show…

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For $\gamma \in (0,2)$, the quantum disk and $\gamma$-quantum wedge are two of the most natural types of Liouville quantum gravity (LQG) surfaces with boundary. These surfaces arise as scaling limits…

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