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Random Structures
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James Murphy, RLM 12.166: Doeblin Trees
Wednesday, February 13, 2019, 03:30pm - 04:30pm
This talk is centered on the random graph generated by a Doeblin-typecoupling of discrete time processes on a countable state spacewhereby when two paths meet, they merge. This random graph isstudied through a novel subgraph, called a bridge graph, generatedby paths started in a fixed state at any time. The bridge graphis made into a unimodular network by marking it and selectinga root in a specified fashion. The unimodularity of this networkis leveraged to discern global properties of the larger Doeblingraph. Bi-recurrence, i.e., recurrence both forwards and backwardsin time, is introduced and shown to be a key property in uniquelydistinguishing paths in the Doeblin graph, and also a decisiveproperty for Markov chains indexed by $\mathbb{Z}$. Propertiesrelated to simulating the bridge graph are also studied. Thisis joint work with Fran?ois Baccelli and Mir-Omid Haji-Mirsadeghi.The preprint is available at https://arxiv.org/abs/1811.10058
Location: RLM 12.166

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