4 citations · 4 across the 3 of their papers we have counts for
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Local limits of bipartite maps with prescribed face degrees in high genus
Thomas Budzinski, Baptiste Louf
We study the local limits of uniform high genus bipartite maps with prescribed face degrees. We prove the convergence towards a family of infinite maps of the plane, the q-IBPMs, w…
Recurrence of the Uniform Infinite Half-Plane Map via duality of resistances
Thomas Budzinski, Thomas Lehéricy
We study the simple random walk on the Uniform Infinite Half-Plane Map, which is the local limit of critical Boltzmann planar maps with a large and simple boundary. We prove that t…
Universality for random surfaces in unconstrained genus
Thomas Budzinski, Nicolas Curien, Bram Petri
Starting from an arbitrary sequence of polygons whose total perimeter is , we can build an (oriented) surface by pairing their sides in a uniform fashion. Chmutov and Pittel (a…
Supercritical causal maps : geodesics and simple random walk
Thomas Budzinski
We study the random planar maps obtained from supercritical Galton--Watson trees by adding the horizontal connections between successive vertices at each level. These are the hyper…
Infinite geodesics in hyperbolic random triangulations
Thomas Budzinski
We study the structure of infinite geodesics in the Planar Stochastic Hyperbolic Triangulations , which are the hyperbolic analogs of the UIPT. We prove that these ge…