A. Járai & D. Mata López: Electrical resistance of the Branching Random Walk trace in low-dimensions and in dimension 6.

Abstract: We study the trace of the incipient infinite oriented branching random walk in \mathbb{Z}^d \times \mathbb{Z}_+ when the dimension is d = 6. Under suitable​ moment assumptions, we show that ​the electrical resistance between the root and level n​ is O(n \log^{-\xi}n ) for a \xi > 0 that does not depend ​on details of the model. The proof is based on an adaptation of the induction argument of Járai and Nachmias (2014), that showed that the resistance is O(n^{1-\alpha}) when d \le 5. In the first talk we discuss the induction setup when d \le 5. The second talk will explain the required modifications when d = 6.


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