On one property of distances in the infinite random quadrangulation

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P. Chassaing, B. Durhuus. Local limit of labelled trees and expected volume growth in a random quadrangulation. Ann. Probab., vol 34, no. 3, 879–917, 2006. arXiv:math/0311532

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J-F. Le Gall. The topological structure of scaling limits of large planar maps. Invent. Math., vol 169 no 3, 621–670, 2007. arXiv:math/0607567

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J.-F. Marckert, G. Miermont. Invariance principles for random bipartite planar maps. Ann. Probab., vol 35, no. 5, 1642–1705, 2007. arXiv:math/0504110

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