163 citations · 1.4k across the 76 of their papers we have counts for
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Counting mobiles by integrable systems
Michel Bergère, Bertrand Eynard, Emmanuel Guitter +1
Mobiles are a particular class of decorated plane trees which serve as codings for planar maps. Here we address the question of enumerating mobiles in their most general flavor, in…
Hamiltonian cycles on bicolored random planar maps
Bertrand Duplantier, Olivier Golinelli, Emmanuel Guitter
We study the statistics of Hamiltonian cycles on various families of bicolored random planar maps (with the spherical topology). These families fall into two groups corresponding t…
Exponents for Hamiltonian paths on random bicubic maps and KPZ
Philippe Di Francesco, Bertrand Duplantier, Olivier Golinelli +1
We evaluate the configuration exponents of various ensembles of Hamiltonian paths drawn on random planar bicubic maps. These exponents are estimated from the extrapolations of exac…
Arctic curves of the twenty-vertex model with domain wall boundaries
Bryan Debin, Philippe Di Francesco, Emmanuel Guitter
We use the tangent method to compute the arctic curve of the Twenty-Vertex (20V) model with particular domain wall boundary conditions for a wide set of integrable weights. To this…
The Arctic curve for Aztec rectangles with defects via the Tangent Method
Philippe Di Francesco, Emmanuel Guitter
The Tangent Method of Colomo and Sportiello is applied to the study of the asymptotics of domino tilings of large Aztec rectangles, with some fixed distribution of defects along a…
A tangent method derivation of the arctic curve for q-weighted paths with arbitrary starting points
Philippe Di Francesco, Emmanuel Guitter
We use a tangent method approach to obtain the arctic curve in a model of non-intersecting lattice paths within the first quadrant, including a q-dependent weight associated with t…