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math-ph2009★ 59 cited
Duality and KPZ in Liouville Quantum Gravity
Bertrand Duplantier, Scott Sheffield
We present a (mathematically rigorous) probabilistic and geometrical proof of the KPZ relation between scaling exponents in a Euclidean planar domain D and in Liouville quantum gra…
math-ph2006★ 64 cited
Conformal Random Geometry
Bertrand Duplantier
In these Notes, a comprehensive description of the universal fractal geometry of conformally-invariant scaling curves or interfaces, in the plane or half-plane, is given. The prese…