Bibliography
Monography Chapter
The Brownian web, the Brownian net, and their universality
, ,
: Advances in Disordered Systems, Random Processes and Some Applications, p. 270-368 , Eds: Contucci Pierluigi, Giardina Cristian
: GA15-08819S, GA ČR
: Brownian net, Brownian web, universality
: http://library.utia.cas.cz/separaty/2017/SI/swart-0476050.pdf
(eng): The Brownian web is a collection of one-dimensional coalescing Brownian motions starting from everywhere in space and time, and the Brownian net is a generalization that also allows branching. They appear in the diffusive scaling limits of many one-dimensional interacting particle systems with branching and coalescence. This article gives an introduction to the Brownian web and net, and how they arise in the scaling limits of various one-dimensional models, focusing mainly on coalescing random walks and random walks in i.i.d. space-time random environments. We will also briefly survey models and results connected to the Brownian web and net, including alternative topologies, population genetic models, true self-repelling motion, planar aggregation, drainage networks, oriented percolation, black noise and critical percolation. Some open questions are discussed at the end.
: BA
: 10101