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We consider “weaves” – loosely, a weave is a set of non-crossing cadlag paths that covers 1+1 dimensional space-time. Here, we do not require any particular distribution for the particle motions. Weaves are a general class of random processes, of which the Brownian web is a canonical example; just as Brownian motion is a canonical example of a (single) random path. It turns out that the space of weaves has an interesting geometric structure in its own right, which will be the focus of the talk. This structure provides key information that leads to an accessible theory of weak convergence for general weaves. Joint work with Jan Swart.
