Universal Random Structures in 2D

Readings

• Revuz, and Yor. Continuous Martingales and Brownian Motion . Springer, 2004. ISBN: 9783540643258.
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• Bertoin. Levy Processes . Cambridge University Press, 1998. ISBN: 9780521646321.
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• Curien, and Kortchemski. “ Stable Loop Trees .” Electronic Journal of Probability 19, no. 108 (2014): 1–35. ↗
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• Aldous. “ Continuum Random Tree I .” The Annals of Probability 19, no. 1 (1991): 1–28. ↗
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• ———. “ The Continuum Random Tree III .” The Annals of Probability 21, no. 1 (1993): 248–89. ↗
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• Timorin. “Moore’s Theorem.” (PDF) 2012. ↗
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• Le Gall, and Miermont. “ Scaling Limits of Random Trees and Planar Maps .” 2011. ↗
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• Le Gall. “ Random Geometry on the Sphere .” 2014. ↗
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• Sheffield. “ Quantum Gravity and Inventory Accumulation .” 2011. ↗
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• Miller, Sheffield. “An Axiomatic Characterization of the Brownian Map.” (PDF - 1.2MB) 2015. ↗
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• Sheffield. “ Gaussian Free Fields for Mathematicians .” 2003. ↗
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• Werner. “Topics on the Two-dimensional Gaussian Free Field.” (PDF) 2014. ↗
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• Duplantier, Rhodes, et al. “Log-correlated Free Field in General Dimension.” (PDF) 2014. ↗
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• Lodhia, Sheffield, et al. “Fractional Gaussian Fields: A Survey.” (PDF - 3.3MB) 2016. ↗
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• Duplantier, and Sheffield. “ Liouville Quantum Gravity and KPZ .” 2010. ↗
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• Garban. “ Quantum Gravity and the KPZ Formula .” 2012. ↗
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• Werner. “ Random Planar Curves and Schramm-Loewner Evolutions .” 2003. ↗
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• Kager, and Bernard. “ A Guide to Stochastic Loewner Evolution and its Applications .” Journal of Statistical Physics 115, no. 5 (2004): 1149–229. ↗
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• Witten, and Sander. “Diffusion Limited Aggregation.” (PDF - 1.7MB) The American Physical Society 27, no. 9 (1983). ↗
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• Kesten. “ DLA Bounds .” Stochastic Processes and their Applications 25 (1987): 165–84. ↗
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• Niemeyer, Pietronero, et al. “Dielectric Breakdown Model.” (PDF) Physical Review Letter 52, no. 12 (1984). ↗
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• Quaste. “Introduction to KPZ.” (PDF) Current Development in Mathematics , 2011. ↗
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• Corwin. “ The Kardar–Parisi–Zhang Equation and Universality Class .” Random Matrices: Theory and Applications 1, no. 1 (2012). ↗
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• 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. ↗
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• Chatterjee. “Large N Lattice Gauge Theory.” (PDF) 2016. ↗
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• Levy. “ Large N Master Field in 2D .” 2012. ↗
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• Miller, and Sheffield. “ Imaginary Geometry I: Interacting SLEs .” 2012. (See also parts II, III, IV) ↗
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• Schramm, and Sheffield. “ A Contour Line of the Continuum Gaussian Free Field .” 2010. ↗
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• Sheffield. “ Conformal Weldings of Random Surfaces: SLE and the Quantum Gravity Zipper .” 2015. ↗
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• Miller, and Sheffield. “ Liouville Quantum Gravity as a Mating of Trees .” 2014. ↗
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• Miller, and Sheffield. “ Quantum Loewner Evolution .” 2013. ↗
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