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Conference Papers Year : 2001

Random Triangulations and Planar Maps


Random triangulations or more generally random planar maps have proved useful as an alternative to regular lattices for the definition and study of some simple discrete models of physics. On the other hand, some classical problems in enumeration (e.g. for alternating knots or plane "meanders") can be recasted as discrete models on random lattices. A natural question when introduced to these models is first to understand the random lattice itself: how does it look like in the limit? I will discuss some combinatorial characteristics for which results or conjectures are available. Although some of these results have been derived by physicists using matrix models, the few ingredients of proofs that I might mention will rely on a different approach. Indeed, following the work of W. Tutte in the sixties, the properties of random planar maps have been studied in enumerative combinatorics via decompositions and generating functions.


Other [cs.OH]
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inria-00100681 , version 1 (26-09-2006)


  • HAL Id : inria-00100681 , version 1


Gilles Schaeffer. Random Triangulations and Planar Maps. Séminaire du groupe Theory de Microsoft Research, 2001, Seattle, USA. ⟨inria-00100681⟩
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