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

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