Geodesic distance in planar graphs

Nuclear Physics B

Volumn 663, Issue 3, 2003, Pages 535-567

  Bouttier, J ^a   Di Francesco, Philippe ^a   Guitter, E ^a  

^a CEA SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038498091     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(03)00355-9     Document Type: Article

References (28)

1. Tutte W. A census of planar triangulations Canad. J. Math. 14 1962 21-38
2. Tutte W. A census of Hamiltonian polygons Canad. J. Math. 14 1962 402-417
3. Tutte W. A census of slicings Canad. J. Math. 14 1962 708-722
4. Tutte W. A census of planar maps Canad. J. Math. 15 1963 249-271
5. Brézin E. Itzykson C. Parisi G. Zuber J.-B. Planar diagrams Commun. Math. Phys. 59 1978 35-51
6. Di Francesco P. Ginsparg P. Zinn-Justin J. 2D gravity and random matrices Phys. Rep. 254 1995 1-131
7. Eynard B. Random matrices Saclay Lecture Notes (2000) http://www-spht.cea.fr/lectures_notes.shtml
8. Knizhnik V.G. Polyakov A.M. Zamolodchikov A.B. Fractal structure of 2D quantum gravity Mod. Phys. Lett. A 3 1988 819-826
9. David F. Conformal field theories coupled to 2D gravity in the conformal gauge Mod. Phys. Lett. A 3 1988 1651-1656
10. Distler J. Kawai H. Conformal field theory and 2D quantum gravity Nucl. Phys. B 321 1989 509-527
11. Kawai H. Kawamoto N. Mogami T. Watabiki Y. Transfer matrix formalism for two-dimensional quantum gravity and fractal structures of spacetime Phys. Lett. B 306 1993 19-26
12. Ambjørn J. Watabiki Y. Scaling in quantum gravity Nucl. Phys. B 445 1995 129-144
13. Ambjørn J. Jurkiewicz J. Watabiki Y. On the fractal structure of two-dimensional quantum gravity Nucl. Phys. B 454 1995 313-342
14. Chassaing P. Schaeffer G. Random planar lattices and integrated super-Brownian excursion math.CO/0205226
15. Schaeffer G. Bijective census and random generation of Eulerian planar maps Electron. J. Combin. 4 1997 R20
16. See also, G. Schaeffer, Conjugaison d'arbres et cartes combinatoires aléatoires, PhD Thesis, Université Bordeaux I (1998)
17. Bouttier J. Di Francesco P. Guitter E. Census of planar maps: from the one-matrix model solution to a combinatorial proof Nucl. Phys. B 645 2002 477-499
18. Bousquet-Mélou M. Schaeffer G. Enumeration of planar constellations Adv. Appl. Math. 24 2000 337-368
19. Jimbo M. Miwa T. Solitons and infinite-dimensional Lie algebras Publ. Res. Inst. Math. Sci. Kyoto Univ. 19 3 1983 943-1001
20. Staudacher M. The Yang-Lee edge singularity on a dynamical planar random surface Nucl. Phys. B 336 1990 349-362
21. Gelfand I. Dikii L. Fractional powers of operators and Hamiltonian systems Funct. Anal. Appl. 10 4 1976 13
22. Kawamoto N. Yotsuji K. Numerical study for the c-dependence of fractal dimension in two-dimensional quantum gravity Nucl. Phys. B 644 2002 533-567
23. Bouttier J. Di Francesco P. Guitter E. Counting colored random triangulations Nucl. Phys. B 641 2002 519-532
24. Bousquet-Mélou M. Schaeffer G. The degree distribution in bipartite planar maps: application to the Ising model math.CO/0211070
25. Bouttier J. Di Francesco P. Guitter E. Combinatorics of hard particles on planar maps Nucl. Phys. B 655 2002 313-341
26. J. Bouttier, P. Di Francesco, E. Guitter, in preparation
27. Delmas J.-F. Computation of moments for the length of the one dimensional ISE support (2002) http://cermics.enpc.fr/~delmas/
28. Di Francesco P. Guitter E. Critical and multicritical semi-random (1+d)-dimensional lattices and hard objects in d dimensions J. Phys. A: Math. Gen. 35 2002 897-927