7 citations · 10 across the 5 of their papers we have counts for
5 papers · 1 filter
The Brownian plane
Nicolas Curien, Jean-François Le Gall
We introduce and study the random non-compact metric space called the Brownian plane, which is obtained as the scaling limit of the uniform infinite planar quadrangulation. Alterna…
The Liouville and the intersection properties are equivalent for planar graphs
Itai Benjamini, Nicolas Curien, Agelos Georgakopoulos
It is shown that if a planar graph admits no non-constant bounded harmonic functions then the trajectories of two independent simple random walks intersect almost surely.
Simple random walk on the uniform infinite planar quadrangulation: Subdiffusivity via pioneer points
Itai Benjamini, Nicolas Curien
We study the pioneer points of the simple random walk on the uniform infinite planar quadrangulation (UIPQ) using an adaptation of the peeling procedure of Angel to the quadrangula…
Uniform infinite planar quadrangulations with a boundary
Nicolas Curien, Grégory Miermont
We introduce and study the uniform infinite planar quadrangulation (UIPQ) with a boundary via an extension of the construction of arXiv:1201.1052. We then relate this object to its…
Partial Match Queries in Two-Dimensional Quadtrees : a Probabilistic Approach
Nicolas Curien, Adrien Joseph
We analyze the mean cost of the partial match queries in random two-dimensional quadtrees. The method is based on fragmentation theory. The convergence is guaranteed by a coupling…