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タイトル: | Scaling limit of a biased random walk on a critical branching random walk (Stochastic Analysis on Large Scale Interacting Systems) |
著者: | Andriopoulos, George |
キーワード: | 60K37 60F17 82D30 random walk in random environment diffusion in random potential biased random walk branching random walk Galton-Watson tree Sinai's regime |
発行日: | Apr-2020 |
出版者: | Research Institute for Mathematical Sciences, Kyoto University |
誌名: | 数理解析研究所講究録別冊 |
巻: | B79 |
開始ページ: | 163 |
終了ページ: | 177 |
抄録: | Relying on powerful resistance techniques developed in [8], the recent paper `Invariance principles for random walks in random environment on trees' [4] investigates random walks in random environment on tree-like spaces and their scaling limits in a certain regime, that is when the potential of the random walk in random environment converges. We introduce and summarise a result from [4]. We choose to review the example of a novel scaling continuum limit of a biased random walk on large critical branching random walk. In this case the diffusion that is not on natural scale is identified as a Brownian motion on a continuum random fractal tree with its canonical metric replaced by a distorted resistance metric. This example allows the least technical presentation (compared to the others covered in the main article). Moreover, it is nevertheless of current interest, given its relation to critical percolation. |
記述: | "Stochastic Analysis on Large Scale Interacting Systems". November 5-8, 2018. edited by Ryoki Fukushima, Tadahisa Funaki, Yukio Nagahata, Hirofumi Osada and Kenkichi Tsunoda. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. |
著作権等: | © 2020 by the Research Institute for Mathematical Sciences, Kyoto University. All rights reserved. |
URI: | http://hdl.handle.net/2433/260650 |
出現コレクション: | B79 Stochastic Analysis on Large Scale Interacting Systems |
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