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Title: Scaling limit of a biased random walk on a critical branching random walk (Stochastic Analysis on Large Scale Interacting Systems)
Authors: Andriopoulos, George
Keywords: 60K37
60F17
82D30
random walk in random environment
diffusion in random potential
biased random walk
branching random walk
Galton-Watson tree
Sinai's regime
Issue Date: Apr-2020
Publisher: Research Institute for Mathematical Sciences, Kyoto University
Journal title: 数理解析研究所講究録別冊
Volume: B79
Start page: 163
End page: 177
Abstract: 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.
Description: "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.
Rights: © 2020 by the Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.
URI: http://hdl.handle.net/2433/260650
Appears in Collections:B79 Stochastic Analysis on Large Scale Interacting Systems

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