Exponents for Hamiltonian paths on random bicubic maps and KPZ

Autor: Philippe Di Francesco, Bertrand Duplantier, Olivier Golinelli, Emmanuel Guitter

Publikováno v: Nuclear Physics B, Vol 987, Iss , Pp 116084- (2023)

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 exact enumeration results for finite sizes and compared with their theoret

Externí odkaz: https://doaj.org/article/16dc649aee8046ddae64a2680515cb8e

Maps of unfixed genus and blossoming trees

Autor: Éric Fusy, Emmanuel Guitter

Publikováno v: Advances in Applied Mathematics
Advances in Applied Mathematics, 2021, 129, pp.102208. ⟨10.1016/j.aam.2021.102208⟩
Advances in Applied Mathematics, Elsevier, 2021, 129, pp.102208

We introduce bijections between families of rooted maps with unfixed genus and families of so-called blossoming trees endowed with an arbitrary forward matching of their leaves. We first focus on Eulerian maps with controlled vertex degrees. The mapp

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::70a0647648da2975e77a3dbb8e9deff7

Arctic curves of the twenty-vertex model with domain wall boundaries

Autor: Emmanuel Guitter, Philippe Di Francesco, Bryan Debin

Publikováno v: Journal of Statistical Physics
Journal of Statistical Physics, Springer Verlag, 2020, 179, pp.33-89. ⟨10.1007/s10955-020-02518-y⟩
Journal of Statistical Physics, 2020, 179, pp.33-89. ⟨10.1007/s10955-020-02518-y⟩

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 end, we extend to the finite geometry of domain wall boundary conditi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9460859c7a7c384e69685036273472dc
http://arxiv.org/abs/1910.06833

The Arctic curve for Aztec rectangles with defects via the Tangent Method

Autor: 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 boundary. The associated Non-Intersecting Lattice Path configurations

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::822178d84c72bcc99f0e420ab51896f6

Comparing two statistical ensembles of quadrangulations: a continued fraction approach

Autor: Emmanuel Guitter, Éric Fusy

Publikováno v: Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions
Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions, 2017, 4 (2), pp.125-176. ⟨10.4171/AIHPD/37⟩
Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions, European Mathematical Society, 2017, 4 (2), pp.125-176. ⟨10.4171/AIHPD/37⟩

We use a continued fraction approach to compare two statistical ensembles of quadrangulations with a boundary, both controlled by two parameters. In the first ensemble, the quadrangulations are bicolored and the parameters control their numbers of ve

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2d3b493549a0247faa578f2f1532d5e8
https://hal.science/hal-01188331