The moduli of annuli in random conformal geometry
@inproceedings{Ang2022TheMO, title={The moduli of annuli in random conformal geometry}, author={Morris Ang and Guillaume Remy and Xin Sun}, year={2022} }
. 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 the scaling limit of uniformly sampled planar maps with annular topology, which is as predicted from the ghost partition function in bosonic string theory. The second is for the law of the modulus of the annulus bounded by a loop of a simple conformal loop ensemble (CLE) on a disk and the disk…
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References
SHOWING 1-10 OF 145 REFERENCES
The O(n) Model on the Annulus
- Mathematics, Physics
- 2006
We use Coulomb gas methods to derive an explicit form for the scaling limit of the partition function of the critical O(n) model on an annulus, with free boundary conditions, as a function of its…
Theory Related Fields
- 179(1-2):345–406,
- 2021
Liouville quantum gravity as a mating of trees
- Physics
- 2014
There is a simple way to "glue together" a coupled pair of continuum random trees (CRTs) to produce a topological sphere. The sphere comes equipped with a measure and a space-filling curve (which…
Compact Brownian surfaces I: Brownian disks
- Mathematics
- 2015
We show that, under certain natural assumptions, large random plane bipartite maps with a boundary converge after rescaling to a one-parameter family $$(\mathrm {BD}_L,\, 0<L<\infty )$$(BDL,0<L<∞) of…
arXiv e-prints
- page arXiv:2203.11830, March
- 2022
arXiv e-prints
- page arXiv:2107.01788, July
- 2021
Theory Related Fields
- 139(3-4):521–541,
- 2007
ArXiv e-prints
- Apr
- 2021
Duke Math
- J., 169(1):177–211,
- 2020
Existence and uniqueness of the conformally covariant volume measure on conformal loop ensembles
- Mathematics
- 2022
We prove the existence and uniqueness of the canonical conformally covariant volume measure on the carpet/gasket of a conformal loop ensemble (CLEκ, κ P p8{3, 8q) which respects the Markov property…