Zobrazeno 1 - 10
of 39
pro vyhledávání: '"Louf, Baptiste"'
We relate two important notions in graph theory: expanders which are highly connected graphs, and modularity a parameter of a graph that is primarily used in community detection. More precisely, we show that a graph having modularity bounded below 1
Externí odkaz:
http://arxiv.org/abs/2312.07521
We prove that uniform random triangulations whose genus is proportional to their size $n$ have diameter of order $\log n$ with high probability. We also show that in such triangulations, the distances between most pairs of points differ by at most an
Externí odkaz:
http://arxiv.org/abs/2311.04005
Publikováno v:
Ann. Probab. 52 (4), 1253-1359, (July 2024)
We study the asymptotic behaviour of random integer partitions under a new probability law that we introduce, the Plancherel-Hurwitz measure. This distribution, which has a natural definition in terms of Young tableaux, is a deformation of the classi
Externí odkaz:
http://arxiv.org/abs/2206.11315
Autor:
Janson, Svante, Louf, Baptiste
We study uniformly random maps with a single face, genus $g$, and size $n$, as $n,g\rightarrow \infty$ with $g = o(n)$, in continuation of several previous works on the geometric properties of "high genus maps". We calculate the number of short simpl
Externí odkaz:
http://arxiv.org/abs/2111.11903
We study the asymptotic behaviour of random factorizations of the $n$-cycle into transpositions of fixed genus $g>0$. They have a geometric interpretation as branched covers of the sphere and their enumeration as Hurwitz numbers was extensively studi
Externí odkaz:
http://arxiv.org/abs/2105.03284
Autor:
Janson, Svante, Louf, Baptiste
We study large uniform random maps with one face whose genus grows linearly with the number of edges, which are a model of discrete hyperbolic geometry. In previous works, several hyperbolic geometric features have been investigated. In the present w
Externí odkaz:
http://arxiv.org/abs/2103.02549
Autor:
Louf, Baptiste
We study large uniform random maps with one face whose genus grows linearly with the number of edges. They can be seen as a model of discrete hyperbolic geometry. In the past, several of these hyperbolic geometric features have been discovered, such
Externí odkaz:
http://arxiv.org/abs/2102.11680
Autor:
Louf, Baptiste, Skerman, Fiona
In this paper, we consider a structural and geometric property of graphs, namely the presence of large expanders. The problem of finding such structures was first considered by Krivelevich [SIAM J. Disc. Math. 32 1 (2018)]. Here, we show that the pro
Externí odkaz:
http://arxiv.org/abs/2012.15722
Autor:
Louf, Baptiste
We study large uniform random quadrangulations whose genus grow linearly with the number of faces, whose local convergence was recently established by Budzinski and the author arXiv:1902.00492,arXiv:2012.05813. Here we study several properties of the
Externí odkaz:
http://arxiv.org/abs/2012.06512
Autor:
Budzinski, Thomas, Louf, Baptiste
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, which exhibit both a spatial Markov property and a hyperbolic behaviour
Externí odkaz:
http://arxiv.org/abs/2012.05813