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math-ph2008★ 38 cited
The three-point function of planar quadrangulations
J. Bouttier, E. Guitter
We compute the generating function of random planar quadrangulations with three marked vertices at prescribed pairwise distances. In the scaling limit of large quadrangulations, th…
math-ph2007★ 21 cited
Statistics of geodesics in large quadrangulations
J. Bouttier, E. Guitter
We study the statistical properties of geodesics, i.e. paths of minimal length, in large random planar quadrangulations. We extend Schaeffer's well-labeled tree bijection to the ca…