Random walks on random graphs in critical regimes

关键状态下随机图上的随机游走

• 批准号: 18H05832
• 负责人: Croydon David
• 金额: $ 1.91万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Research Activity Start-up
• 财政年份: 2018
• 资助国家: 日本
• 起止时间: 2018-08-24 至 2020-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-18H05832/
• 关键词: random walks; random graphs; fractals; random walk; uniform spanning tree; percolation; scaling limit; fractal

On a visit to the University of Melbourne, I completed an article 'Biased random walk on the trace of biased random walk on the trace of...' with Mark Holmes, which has been submitted. I have also made progress on several ongoing projects, including: together with Daisuke Shiraishi (Kyoto), Omer Angel (UBC), and Sarai Hernandez Torres (UBC), I have work on the random walk on the 3-dimensional uniform spanning tree - we expect to complete this in FY2019, following a visit to UBC in September; I also hope to complete there a project that has been ongoing this year with Martin Barlow (UBC) and Takashi Kumagai (Kyoto University) on the two-dimensional model.

在访问墨尔本大学，我完成了一篇文章“有偏随机游走的痕迹有偏随机游走的痕迹...与马克·霍姆斯的合作已经提交我还在几个正在进行的项目上取得了进展，包括：与Daisuke Shiraishi（京都），奥默天使（UBC）和萨莱埃尔南德斯托雷斯（UBC）一起，我在三维均匀生成树上的随机行走方面取得了进展-我们预计在2019财年完成这项工作，在9月份访问UBC之后;我还希望在那里完成一个项目，该项目今年一直在进行中，与马丁巴洛（UBC）和熊谷隆（京都大学）的二维模型。

项目成果

Scaling limits of stochastic processes associated with resistance forms

• DOI: 10.1214/17-aihp861
• 发表时间: 2016-09
• 期刊: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
• 作者: D. Croydon

Biased random walk on the trace of biased random walk

有偏随机游走迹上的有偏随机游走

• 发表时间: 2018
• 作者: 加藤百合;諫田泰成;西田基宏;David Croydon
• 通讯作者: David Croydon

Random walks on fractals and critical random graphs

分形和临界随机图上的随机游走

• 发表时间: 2019
• 作者: Hamada Hidetaka;Iancu Mihai;Kohr Gabriela;Sawano Yoshihiro;David Croydon
• 通讯作者: David Croydon

Scaling limits and heat kernel estimates for stochastic processes associated with resistance forms

与阻力形式相关的随机过程的标度限制和热核估计

• 发表时间: 2018
• 作者: Y. Oku;K. Nagamine;I. Shimizu;Yoshihiro Shibata;山田 澄生;Croydon David
• 通讯作者: Croydon David