### Selected References on Universal Objects

#### Overview

#### Continuum Random Tree References

- Duquesne, and Le Gall. “Random Trees, Levy processes, and Spatial Branching Processes.” (PDF)
- Lalley. “Levy Processes, Stable Processes, and Subordinators.” (PDF)
- Lawler. “Bessel Processes.” (PDF)
- Revuz, and Yor.
*Continuous Martingales and Brownian Motion*. Springer, 2004. ISBN: 9783540643258. - Bertoin.
*Levy Processes*. Cambridge University Press, 1998. ISBN: 9780521646321. - Johnson. “Poisson Point Proccesses.” (PDF - 2.5MB)
- Curien, and Kortchemski. “Stable Loop Trees.”
*Electronic Journal of Probability*19, no. 108 (2014): 1–35. - Aldous. “Continuum Random Tree I.”
*The Annals of Probability*19, no. 1 (1991): 1–28. - ———. “Continuum Random Tree II.” (PDF)
- ———. “The Continuum Random Tree III.”
*The Annals of Probability*21, no. 1 (1993): 248–89. - Mörters, and Peres. “Brownian Motion.” (PDF - 7.2MB)
- Timorin. “Moore’s Theorem.” (PDF) 2012.

#### Random Planar Maps and the Brownian Map References

- Le Gall, and Miermont. “Scaling Limits of Random Trees and Planar Maps.” 2011.
- Le Gall. “Random Geometry on the Sphere.” 2014.
- Bernardi. “Slides on Cori-Vauquelin-Schaeffer Bijection.” (PDF - 1.5MB) and “Brownian Map Convergence.” (PDF - 1.7MB)
- Sheffield. “Quantum Gravity and Inventory Accumulation.” 2011.
- Miller, Sheffield. “An Axiomatic Characterization of the Brownian Map.” (PDF - 1.2MB) 2015.

#### Gaussian Free Field References

- Sheffield. “Gaussian Free Fields for Mathematicians.” 2003.
- Werner. “Topics on the Two-dimensional Gaussian Free Field.” (PDF) 2014.
- Duplantier, Rhodes, et al. “Log-correlated Free Field in General Dimension.” (PDF) 2014.
- Lodhia, Sheffield, et al. “Fractional Gaussian Fields: A Survey.” (PDF - 3.3MB) 2016.

#### Liouville Quantum Gravity References

- Duplantier, and Sheffield. “Liouville Quantum Gravity and KPZ.” 2010.
- Garban. “Quantum Gravity and the KPZ Formula.” 2012.
- Berestycki. “Introduction to the Gaussian Free Field and Liouville Quantum Gravity.” (PDF - 2.8MB)

#### Schramm-Loewner Evolution and Discrete Analogs References

- Werner. “Random Planar Curves and Schramm-Loewner Evolutions.” 2003.
- Lawler. “Conformally Invariant Processes in the Plane: Summer School Lecture Notes.” (PDF)
- “Conformally Invariant Processes in the Plane: Book.” (PS - 1.7MB) (Lawler—save and use online ps2pdf if your machine doesn’t have postscript).
- Kager, and Bernard. “A Guide to Stochastic Loewner Evolution and its Applications.”
*Journal of Statistical Physics*115, no. 5 (2004): 1149–229. - Berestycki, N., and J. R. Norris. “Lectures on Schramm-Loewner Evolution.” (PDF)

#### Growth Models References

- Witten, and Sander. “Diffusion Limited Aggregation.” (PDF - 1.7MB)
*The American Physical Society*27, no. 9 (1983). - Kesten. “DLA Bounds.”
*Stochastic Processes and their Applications*25 (1987): 165–84. - Niemeyer, Pietronero, et al. “Dielectric Breakdown Model.” (PDF)
*Physical Review Letter*52, no. 12 (1984). - Quaste. “Introduction to KPZ.” (PDF)
*Current Development in Mathematics*, 2011. - Corwin, Quastel, et al. “Renormalization Fixed Point of the KPZ Universality Class.” (PDF)
- Corwin. “The Kardar–Parisi–Zhang Equation and Universality Class.”
*Random Matrices: Theory and Applications*1, no. 1 (2012). - Borowin, Corwin, et al. “Free Energy Fluctuations for Directed Polymers in Random Media in 1 + 1 Dimension.”
*Communications on Pure and Applied Mathematics*67, no. 7 (2014): 1129–214.

#### Yang Mills References

- Jaffe, and Witten. “Quantum Yang-Mills Theory.” (PDF)
- Chatterjee. “Large N Lattice Gauge Theory.” (PDF) 2016.
- Levy. “Large N Master Field in 2D.” 2012.

### Selected References on Universal Object Relationships

#### GFF + SLE

- Miller, and Sheffield. “Imaginary Geometry I: Interacting SLEs.” 2012. (See also parts II, III, IV)
- Schramm, and Sheffield. “A Contour Line of the Continuum Gaussian Free Field.” 2010.

#### 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)