18.177 | Fall 2015 | Graduate

Universal Random Structures in 2D

Readings

Selected References on Universal Objects

Overview

Continuum Random Tree References

Random Planar Maps and the Brownian Map References

Gaussian Free Field References

Liouville Quantum Gravity References

Schramm-Loewner Evolution and Discrete Analogs References

Growth Models References

Yang Mills References

Selected References on Universal Object Relationships

GFF + SLE

LQG + LQG = LQG + SLE

Sheffield. “Conformal Weldings of Random Surfaces: SLE and the Quantum Gravity Zipper.” 2015.

CRT + CRT = LQG + SLE

Miller, and Sheffield. “Liouville Quantum Gravity as a Mating of Trees.” 2014.

LQG + Reshuffled SLE = LQG + DBM

Miller, and Sheffield. “Quantum Loewner Evolution.” 2013.

LQG = TBM

Miller, and Sheffield. “Liouville Quantum Gravity and the Brownian Map.” (PDF)

Course Info

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Fall 2015
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