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A version of the random directed forest and its convergence to the Brownian web. (arXiv:1704.05555v2 [math.PR] UPDATED)
来源于:arXiv
Several authors have studied convergence in distribution to the Brownian web
under diffusive scaling of Markovian random walks. In a paper by R. Roy, K.
Saha and A. Sarkar, convergence to the Brownian web is proved for a system of
coalescing random paths - the Random Directed Forest- which are not Markovian.
Paths in the Random Directed Forest do not cross each other before coalescence.
Here we study a generalization of the non-Markovian Random Directed Forest
where paths can cross each other and prove convergence to the Brownian web.
This provides an example of how the techniques to prove convergence to the
Brownian web for systems allowing crossings can be applied to non-Markovian
systems. 查看全文>>