Two-dimensional Poisson Trees converge to the Brownian web
By Pablo A. Ferrari, L. Fontes, Xian-Yuan Wu. 2003
47 citations recorded by the source corpus.
Abstract The Brownian web can be roughly described as a family of coalescing one-dimensional Brownian motions starting at all times in R and at all points of R . The two-dimensional Poisson tree is a family of continuous time one-dimensional random walks with uniform jumps in a bounded interval. The walks start at the space–time points of a homogeneous Poisson process in R 2 and are in fact constructed as a function of the point process. This tree was introduced by Ferrari, Landim and Thorisson. By verifying criteria derived by Fontes, Isopi, Newman and Ravishankar, we show that, when properly rescaled, and under the topology introduced by those authors, Poisson trees converge weakly to the Brownian web.
Subfields: Finance, Mathematical Physics, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/d9be8e5269d6703e7a96ed9cbb600655b7d4bad6
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Finance
In Mathematical Physics
- Charles Bordenave
- François Baccelli
- L. Fontes
- Charles M. Newman
- Djalil CHAFAÏ
- Wendelin Werner
- F. Augeri
- Benoît Collins
In Molecular Biology
Citations in the corpus
- The Radial Spanning Tree of a Poisson Point Process (2007, background): “This tree holds similarities with the minimal directed spanning tree ([11], [18], [17]) and the Poisson forest (as defined in [9], [8]).”
- The Brownian Web: Characterization and Convergence (2003, methodology): “After rescaling to spatial steps of sizeδ and time steps of sizeδ2, a single rescaled random walk (say, starting from 0 at time 0)Y (δ)0,0(t) = δY0,0(δ−2t) converges asδ → 0 to a standard Brownian motionB(t).”