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We introduce a new construction of the Uniform Infinite Planar Quadrangulation (UIPQ).
On one property of distances in the infinite random quadrangulation
M. Krikun · 1907
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On the classification of noncompact surfaces
I. Richards · 1963
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A census of planar maps
W. T. Tutte · 1963
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Planar maps are well labeled trees
R. Cori and B. Vauquelin · 1981
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Hyperbolic manifolds, groups and actions
M. Gromov · 1981
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On transience and recurrence of generalized random walks
F. M. Dekking · 1982
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Subdiffusive behavior of random walk on a random cluster
H. Kesten · 1986
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Arbres et processus de Galton-Watson
J. Neveu · 1986
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Regular variation
N. H. Bingham, C. M. Goldie, and J. L. Teugels · 1989
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Matrix integrals and map enumeration: an accessible introduction
A. Zvonkin · 1995
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Quantum geometry
J. Ambjørn, B. Durhuus, and T. Jonsson · 1997
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Conjugaison d’arbres et cartes combinatoires aléatoires. phd thesis
G. Schaeffer · 1998
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Spatial branching processes, random snakes and partial differential equations
J.-F. Le Gall · 1999
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Continuous martingales and Brownian motion
D. Revuz and M. Yor · 1999
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Recurrence of distributional limits of finite planar graphs
I. Benjamini and O. Schramm · 2001
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A course in metric geometry
D. Burago, Y. Burago, and S. Ivanov · 2001
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Random trees, Lévy processes and spatial branching processes
T. Duquesne and J.-F. Le Gall · 2002
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A uniformly distributed infinite planar triangulation and a related branching process
M. Krikun · 2004
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Graphs on surfaces and their applications
S. K. Lando and A. Zvonkin · 2004
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Local limit of labeled trees and expected volume growth in a random quadrangulation
P. Chassaing and B. Durhuus · 2006
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Random real trees
J.-F. Le Gall · 2006
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Conditioned Brownian trees
J.-F. Le Gall and M. Weill · 2006
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Processes on unimodular random networks
D. Aldous and R. Lyons · 2007
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Invariance principles for spatial multitype Galton-Watson trees
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Growth and percolation on the uniform infinite planar triangulation
O. Angel · 2003
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Uniform infinite planar triangulation
O. Angel and O. Schramm · 2003
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Planar maps as labeled mobiles
J. Bouttier, P. Di Francesco, and E. Guitter · 2004
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Random planar lattices and integrated superBrownian excursion
P. Chassaing and G. Schaeffer · 2004
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Ergodic theory on stationary random graphs
I. Benjamini and N. Curien
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The Brownian cactus I. scaling limits of discrete cactuses
N. Curien, J.-F. Le Gall, and G. Miermont
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G. Miermont · 2008
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Random planar metrics
I. Benjamini · 2010
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Geodesics in large planar maps and in the Brownian map
J.-F. Le Gall · 2010
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The two uniform infinite quadrangulations of the plane have the same law
L. Ménard · 2010
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