- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:04:49
Annales de l’Institut Henri Poincaré D
Ann. Inst. Henri Poincaré Comb. Phys. Interact.
AIHPD
2308-5827
2308-5835
General
Combinatorics
Quantum theory
10.4171/AIHPD
http://www.ems-ph.org/doi/10.4171/AIHPD
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
3
2016
1
Multi-point functions of weighted cubic maps
Jan
Ambjørn
University of Copenhagen, COPENHAGEN Ø, DENMARK
Timothy
Budd
University of Copenhagen, COPENHAGEN Ø, DENMARK
Random planar maps, quantum gravity, first passage percolation
We study the geodesic two- and three-point functions of random weighted cubic maps, which are obtained by assigning random edge lengths to random cubic planar maps. Explicit expressions are obtained by taking limits of recently established bivariate multi-point functions of general planar maps. We give an alternative interpretation of the two-point function in terms of an Eden model exploration process on a random planar triangulation. Finally, the scaling limits of the multi-point functions are studied, showing in particular that the two- and three-point functions of the Brownian map are recovered as the number of faces is taken to in finity.
Combinatorics
Probability theory and stochastic processes
Statistical mechanics, structure of matter
1
44
10.4171/AIHPD/23
http://www.ems-ph.org/doi/10.4171/AIHPD/23