Probability and Statistical Mechanics in Information Science

course: Conformal Fractal Geometry and Quantum Gravity

speaker: Bertrand Duplantier (CEA & KITP)

abstract: One considers the general class of conformally invariant critical random curves in the plane. The multifractal distribution for the scaling and winding of the electrostatic potential lines near their boundary is derived from two-dimensional quantum gravity techniques. This applies to the O(N) and Potts models, as well as to the SLE (Stochastic Loewner Evolution).

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