Basic Information

Affiliated programs (koza)

• Graduate School of Science, 数学・数理解析専攻 解析数理講座, 准教授

Academic Degree

• Mathematics

Research History

• From Apr. 2019, To Present

  Kyoto University, Research Institute for Mathematical Sciences, Associate Professor
• From Apr. 2018, To Mar. 2019

  Kyoto University, Department of Advanced Mathematical Sciences, Graduate School of Informatics, Associate Professor
• From Jun. 2017, To Mar. 2018

  University of Warwick, Department of Statistics, Reader
• From Sep. 2012, To May 2017

  University of Warwick, Department of Statistics, Associate Professor
• From Sep. 2008, To Aug. 2012

  University of Warwick, Department of Statistics, Assistant Professor
• From Sep. 2006, To Aug. 2008

  University of Warwick, Department of Statistics, Postdoctoral Research Fellow

ID,URL

• J-Global ID

  201501001880666935

• Researcher number

  50824182

• External link

  http://www.kurims.kyoto-u.ac.jp/~croydon/

Website(s) (URL(s))

• http://www.kurims.kyoto-u.ac.jp/~croydon/

researchmap URL

• https://researchmap.jp/7000013558

Research

Research Topics, Overview of the research

• Research Topics

  Probability theory

• Overview of the research

  David Croydon works in probability theory, with his main research interest being in diffusions on random fractals and how such processes can be constructed as scaling limits of related random walks on random graphs. He also has a growing interest in the behaviour of discrete integrable systems started from random initial conditions.

Research Interests

• discrete integrable systems
• fractals
• random walk
• probability theory

Research Areas

• Natural sciences, Mathematical analysis

Papers

• Heat Kernel Fluctuations for Stochastic Processes on Fractals and Random Media

  Sebastian Andres; David Croydon; Takashi Kumagai

  Applied and Numerical Harmonic Analysis, 26 Jun. 2023, Peer-reviewed, Invited

  
• Extremal regime for one-dimensional Mott variable-range hopping

  D. A. Croydon; R. Fukushima; S. Junk

  2023

  
• Aging and sub-aging for one-dimensional random walks amongst random conductances

  D. A. Croydon; D. Kious; C. Scali

  2023

  
• Heat kernel fluctuations and quantitative homogenization for the one-dimensional Bouchaud trap model

  S. Andres; D. A. Croydon; T. Kumagai

  2023

  
• Scaling limit of critical percolation clusters on hyperbolic random half-planar triangulations and the associated random walks

  D. A. Croydon; E. Archer

  2023

  
• Annealed transition density of simple random walk on a high-dimensional loop-erased random walk

  D. A. Croydon; D. Shiraishi; S. Watanabe

  2023

  
• Correction to: Exact value of the resistance exponent for four dimensional random walk trace

  D. A. Croydon; D. Shiraishi

  Probability Theory and Related Fields, 05 Nov. 2022, Peer-reviewed

  
• Biased random walk on supercritical percolation: anomalous fluctuations in the ballistic regime

  Adam M. Bowditch; David A. Croydon

  Electronic Journal of Probability, 01 Jan. 2022, Peer-reviewed

  
• Spectral dimension of simple random walk on a long-range percolation cluster

  V. H. Can; D. A. Croydon; T. Kumagai

  Electronic Journal of Probability, 01 Jan. 2022, Peer-reviewed

  
• Scaling limit for random walk on the range of random walk in four dimensions

  D. A. Croydon; D. Shiraishi

  Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 01 Feb. 2023, Peer-reviewed

  
• On the Stationary Solutions of Random Polymer Models and Their Zero-Temperature Limits

  David A. Croydon; Makiko Sasada

  Journal of Statistical Physics, 25 Jun. 2022, Peer-reviewed

  
• Quenched and averaged tails of the heat kernel of the two-dimensional uniform spanning tree

  M. T. Barlow; D. A. Croydon; T. Kumagai

  Probability Theory and Related Fields, Nov. 2021, Peer-reviewed

  Access this paper :

  
• Generalized Hydrodynamic Limit for the Box–Ball System

  David A. Croydon; Makiko Sasada

  Communications in Mathematical Physics, Apr. 2021, Peer-reviewed

  Access this paper :

  
• The Random Conductance Model with Heavy Tails on Nested Fractal Graphs

  David A. Croydon

  Fractal Geometry and Stochastics VI, 2021, Peer-reviewed

  Access this paper :

  
• Bi-infinite Solutions for KdV- and Toda-Type Discrete Integrable Systems Based on Path Encodings

  David A. Croydon; Makiko Sasada; Satoshi Tsujimoto

  Mathematical Physics, Analysis and Geometry, 22 Oct. 2022, Peer-reviewed

  
• Anomalous scaling regime for one-dimensional Mott variable-range hopping

  David A. Croydon; Ryoki Fukushima; Stefan Junk

  The Annals of Applied Probability, 01 Oct. 2023, Peer-reviewed

  
• Detailed balance and invariant measures for discrete KdV- and Toda-type systems

  D. A. Croydon; M. Sasada

  Jul. 2020

  
• Biased Random Walk on the Trace of Biased Random Walk on the Trace of …

  David Croydon; Mark Holmes

  Communications in Mathematical Physics, Apr. 2020, Peer-reviewed

  Access this paper :

  
• Scaling limits of the three-dimensional uniform spanning tree and associated random walk

  O. Angel; D. A. Croydon; S. Hernandez-Torres; D. Shiraishi

  The Annals of Probability, 01 Nov. 2021, Peer-reviewed

  
• The number of spanning clusters of the uniform spanning tree in three dimensions

  Omer Angel; David A. Croydon; Sarai Hernandez-Torres; Daisuke Shiraishi

  Proceeding of "The 12th Mathematical Society of Japan, Seasonal Institute (MSJ-SI) Stochastic Analysis, Random Fields and Integrable Probability.", Jan. 2021, Peer-reviewed, Invited

  
• Discrete integrable systems and Pitman's transformation

  David A. Croydon; Makiko Sasada

  Proceeding of "The 12th Mathematical Society of Japan, Seasonal Institute (MSJ-SI) Stochastic Analysis, Random Fields and Integrable Probability.", Jan. 2021, Peer-reviewed, Invited

  
• Dynamics of the ultra-discrete Toda lattice via Pitman's transformation

  David A. Croydon; Makiko Sasada; Satoshi Tsujimoto

  RIMS Kôkyûroku Bessatsu, 2020, Peer-reviewed, Invited

  
• Duality between box-ball systems of finite box and/or carrier capacity

  David A. Croydon; Makiko Sasada

  RIMS Kôkyûroku Bessatsu, 2020, Peer-reviewed, Invited

  
• Invariant measures for the box-ball system based on stationary Markov chains and periodic Gibbs measures

  David Croydon; Makiko Sasada

  Journal of Mathematical Physics, 2019, Peer-reviewed

  
• An introduction to the trapping experienced by biased random walk on the trace of biased random walk

  David Croydon

  RIMS Kokyuroku, 2019

  
• Dynamics of the Box-Ball System with Random Initial Conditions via Pitman’s Transformation

  David Croydon; Tsuyoshi Kato; Makiko Sasada; Satoshi Tsujimoto

  Memoirs of the American Mathematical Society, Mar. 2023, Peer-reviewed

  
• Scaling limits of stochastic processes associated with resistance forms

  D. A. Croydon

  Ann. Inst. H. Poincare Probab. Statist., 2018, Peer-reviewed

  
• CENTRAL LIMIT THEOREMS FOR THE SPECTRA OF CLASSES OF RANDOM FRACTALS

  Philippe H. A. Charmoy; David A. Croydon; Ben M. Hambly

  TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, Dec. 2017, Peer-reviewed

  
• Heat kernel estimates for FIN processes associated with resistance forms

  D.A. Croydon; B.M. Hambly; T. Kumagai

  Stochastic Processes and their Applications, Sep. 2019, Peer-reviewed

  
• Quenched localisation in the Bouchaud trap model with slowly varying traps

  David A. Croydon; Stephen Muirhead

  PROBABILITY THEORY AND RELATED FIELDS, Jun. 2017, Peer-reviewed

  
• An introduction to stochastic processes associated with resistance forms and their scaling limits

  David A. Croydon

  RIMS Kokyuroku, 2017

  
• SUBSEQUENTIAL SCALING LIMITS OF SIMPLE RANDOM WALK ON THE TWO-DIMENSIONAL UNIFORM SPANNING TREE

  M. T. Barlow; D. A. Croydon; T. Kumagai

  ANNALS OF PROBABILITY, Jan. 2017, Peer-reviewed

  
• Time-changes of stochastic processes associated with resistance forms

  David Croydon; Ben Hambly; Takashi Kumagai

  ELECTRONIC JOURNAL OF PROBABILITY, 2017, Peer-reviewed

  
• Quenched localisation in the Bouchaud trap model with regularly varying traps

  David Croydon; Stephen Muirhead

  RIMS Kokyuroku Bessatsu, 2016, Peer-reviewed

  
• QUENCHED INVARIANCE PRINCIPLES FOR RANDOM WALKS AND ELLIPTIC DIFFUSIONS IN RANDOM MEDIA WITH BOUNDARY

  Zhen-Qing Chen; David A. Croydon; Takashi Kumagai

  ANNALS OF PROBABILITY, Jul. 2015, Peer-reviewed

  
• Functional limit theorems for the Bouchaud trap model with slowly varying traps

  David Croydon; Stephen Muirhead

  STOCHASTIC PROCESSES AND THEIR APPLICATIONS, May 2015, Peer-reviewed

  
• Moduli of continuity of local times of random walks on graphs in terms of the resistance metric

  David A. Croydon

  Trans. Lond. Math. Soc., 2015, Peer-reviewed

  
• Slow movement of a random walk on the range of a random walk in the presence of an external field

  David A. Croydon

  PROBABILITY THEORY AND RELATED FIELDS, Dec. 2013, Peer-reviewed

  
• Biased random walk on critical Galton-Watson trees conditioned to survive

  D. A. Croydon; A. Fribergh; T. Kumagai

  PROBABILITY THEORY AND RELATED FIELDS, Oct. 2013, Peer-reviewed

  
• Scaling Limit for the Random Walk on the Largest Connected Component of the Critical Random Graph

  David A. Croydon

  PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, Jun. 2012, Peer-reviewed

  
• Convergence of mixing times for sequences of random walks on finite graphs

  D. A. Croydon; B. M. Hambly; T. Kumagai

  ELECTRONIC JOURNAL OF PROBABILITY, Jan. 2012, Peer-reviewed

  
• Spectral asymptotics for stable trees

  David Croydon; Ben Hambly

  ELECTRONIC JOURNAL OF PROBABILITY, Nov. 2010, Peer-reviewed

  
• SCALING LIMITS FOR SIMPLE RANDOM WALKS ON RANDOM ORDERED GRAPH TREES

  D. A. Croydon

  ADVANCES IN APPLIED PROBABILITY, Jun. 2010, Peer-reviewed

  
• Random Walk on the Range of Random Walk

  David A. Croydon

  JOURNAL OF STATISTICAL PHYSICS, Jul. 2009, Peer-reviewed

  
• HAUSDORFF MEASURE OF ARCS AND BROWNIAN MOTION ON BROWNIAN SPATIAL TREES

  David A. Croydon

  ANNALS OF PROBABILITY, May 2009, Peer-reviewed

  
• Convergence of simple random walks on random discrete trees to Brownian motion on the continuum random tree

  David Croydon

  ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, Dec. 2008, Peer-reviewed

  
• Local Limit Theorems for Sequences of Simple Random Walks on Graphs

  D. A. Croydon; B. M. Hambly

  POTENTIAL ANALYSIS, Dec. 2008, Peer-reviewed

  
• Random walks on Galton-Watson trees with infinite variance offspring distribution conditioned to survive

  David Croydon; Takashi Kumagai

  ELECTRONIC JOURNAL OF PROBABILITY, Aug. 2008, Peer-reviewed

  
• Self-similarity and spectral asymptotics for the continuum random tree

  David Croydon; Ben Hambly

  STOCHASTIC PROCESSES AND THEIR APPLICATIONS, May 2008, Peer-reviewed

  
• Volume growth and heat kernel estimates for the continuum random tree

  David A. Croydon

  PROBABILITY THEORY AND RELATED FIELDS, Jan. 2008, Peer-reviewed

  
• The Hausdorff dimension of a class of random self-similar fractal trees

  D. A. Croydon

  ADVANCES IN APPLIED PROBABILITY, Sep. 2007, Peer-reviewed

  
• Heat kernel fluctuations for a resistance form with non-uniform volume growth

  D. A. Croydon

  PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, May 2007, Peer-reviewed

  

Awards

• Dec. 2018

  International Consortium of Chinese Mathematicians, Distinguished Paper Award

External funds: Kakenhi

• Stochastic processes associated with resistance forms

  Grant-in-Aid for Scientific Research (C)

  Basic Section 12010:Basic analysis-related

  Kyoto University

  Croydon David

  From 01 Apr. 2019, To 31 Mar. 2024, Granted

  Mott hopping;Extremal process;Random walk;Localization;Random environment;random walk;percolation;subdiffusion;trapping;hear kernel estimates;uniform spanning tree;critical dimension;Mott random walk;heat kernel estimates;scaling limits;scaling limit;random walks;random graphs;fractals

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19K03540/
• Analysis of discrete Integrable systems by probability theory based on Pitman's transformation

  Grant-in-Aid for Scientific Research (B)

  Basic Section 12010:Basic analysis-related

  Kyoto University

  辻本 諭

  From 01 Apr. 2019, To 31 Mar. 2024, Granted

  離散可積分系;確率論;Pitman変換;箱玉系

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19H01792/
• Research on stochastic processes in random media

  Grant-in-Aid for JSPS Fellows

  Basic Section 12010:Basic analysis-related

  University of Tsukuba;Kyoto University

  From 08 Nov. 2019, To 31 Mar. 2022, Granted

  高分子模型;大偏差原理;自由エネルギー;パーコレーション;零温度極限

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19F19814/
• Random walks on random graphs in critical regimes

  Grant-in-Aid for Research Activity Start-up

  0201:Algebra, geometry, analysis, applied mathematics,and related fields

  Kyoto University

  Croydon David

  From 24 Aug. 2018, To 31 Mar. 2020, Project Closed

  random walks;random graphs;fractals;random walk;uniform spanning tree;percolation;scaling limit;fractal

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18H05832/
• Anomalous diffusions on disordered media

  Grant-in-Aid for Scientific Research (A)

  Waseda University;Kyoto University

  Takashi Kumagai

  From 01 Apr. 2017, To 31 Mar. 2022, Project Closed

  確率論;複雑系;数理物理;解析学;ポテンシャル論;統計力学

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17H01093/
• Analysis, geometry and their interplays on fractals and stochastic processes on them

  Grant-in-Aid for Scientific Research (B)

  Basic Section 12010:Basic analysis-related

  Kyoto University

  梶野 直孝

  From 01 Apr. 2022, To 31 Mar. 2027, Granted

  劣ガウス型熱核評価;フラクタル上のポテンシャル論;ランダムフラクタル;自己等角フラクタル;フラクタル上の確率熱方程式;2次元一般化Sierpinski carpet;（劣）ガウス型熱核評価;ランダム媒質中の確率過程;スケール極限;離散群上のランダムウォーク;調和測度;フラクタル上の確率過程

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22H01128/
• Stochastic Processes and Stochastic Analysis on Disordered Media

  Grant-in-Aid for Scientific Research (A)

  Medium-sized Section 12:Analysis, applied mathematics, and related fields

  Waseda University

  熊谷 隆

  From 01 Apr. 2022, To 31 Mar. 2027, Granted

  確率論;複雑系;数理物理;解析学;ポテンシャル論

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22H00099/
• Stochastic processes in random environments with inhomogeneous scaling limits

  Grant-in-Aid for Scientific Research (C)

  Basic Section 12010:Basic analysis-related

  Kyoto University

  Croydon David

  From 01 Apr. 2024, To 31 Mar. 2028, Granted

  random walks;random graphs;fractals;scaling limits;random fields

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-24K06758/
• Analysis, geometry and their interplays on fractals and stochastic processes on them

  Grant-in-Aid for Scientific Research (B)

  Basic Section 12010:Basic analysis-related

  Kyoto University

  梶野 直孝

  From 01 Apr. 2022, To 31 Mar. 2027, Granted

  劣ガウス型熱核評価;フラクタル上のポテンシャル論;ランダムフラクタル;フラクタル上の確率過程;自己等角フラクタル;フラクタル上の確率熱方程式;2次元一般化Sierpinski carpet;（劣）ガウス型熱核評価;ランダム媒質中の確率過程;スケール極限;離散群上のランダムウォーク;調和測度

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23K22399/

External funds: others

• Analysis of ultra-discrete systems based on Pitman’s transformation by probability theory

  Grant-in-Aid for Scientific Research (B)

  From 01 Apr. 2019, To 31 Mar. 2024

  Satoshi Tsujimoto
• Anomalous diffusions on disordered media

  Grant-in-Aid for Scientific Research (A)

  From 01 Apr. 2017, To 31 Mar. 2022

  Takashi Kumagai
• Stochastic processes in random media

  Grant-in-Aid for JSPS Fellows

  From 08 Nov. 2019, To 31 Mar. 2022

  Stefan Junk

Education

Teaching subject(s)

• From 01 Apr. 2024, To 31 Mar. 2025

  ILAS Seminar-E2

  Z002, Spring, Institute for Liberal Arts and Sciences, 2
• From 01 Apr. 2024, To 31 Mar. 2025

  Second Course in Statistics-E2

  N816, Fall, Institute for Liberal Arts and Sciences, 2
• From 01 Apr. 2024, To 31 Mar. 2025

  Mathematical Statistics-E2

  N815, Spring, Institute for Liberal Arts and Sciences, 2
• From 01 Apr. 2024, To 31 Mar. 2025

  Mathematical Statistics-E2

  N815, Fall, Institute for Liberal Arts and Sciences, 2
• From 01 Apr. 2024, To 31 Mar. 2025

  Seminar on Probability Theory b

  1308, Fall, Graduate School of Science, 3
• From 01 Apr. 2024, To 31 Mar. 2025

  Seminar on Probability Theory a

  1307, Spring, Graduate School of Science, 3
• From 01 Apr. 2024, To 31 Mar. 2025

  Seminar on Probability Theory c

  1309, Spring, Graduate School of Science, 3
• From 01 Apr. 2024, To 31 Mar. 2025

  Seminar on Probability Theory d

  1310, Fall, Graduate School of Science, 3
• From 01 Apr. 2023, To 31 Mar. 2024

  ILAS Seminar-E2

  Z002, Spring, Institute for Liberal Arts and Sciences, 2
• From 01 Apr. 2023, To 31 Mar. 2024

  Second Course in Statistics-E2

  N816, Fall, Institute for Liberal Arts and Sciences, 2
• From 01 Apr. 2023, To 31 Mar. 2024

  Mathematical Statistics-E2

  N815, Spring, Institute for Liberal Arts and Sciences, 2
• From 01 Apr. 2023, To 31 Mar. 2024

  Mathematical Statistics-E2

  N815, Fall, Institute for Liberal Arts and Sciences, 2
• From 01 Apr. 2023, To 31 Mar. 2024

  Seminar on Probability Theory a

  1307, Spring, Graduate School of Science, 3
• From 01 Apr. 2023, To 31 Mar. 2024

  Seminar on Probability Theory b

  1308, Fall, Graduate School of Science, 3
• From 01 Apr. 2023, To 31 Mar. 2024

  Seminar on Probability Theory d

  1310, Fall, Graduate School of Science, 3
• From 01 Apr. 2023, To 31 Mar. 2024

  Seminar on Probability Theory c

  1309, Spring, Graduate School of Science, 3
• From 01 Apr. 2022, To 31 Mar. 2023

  Mathematical Statistics-E2

  N815, Spring, Institute for Liberal Arts and Sciences, 2
• From 01 Apr. 2022, To 31 Mar. 2023

  Seminar on Probability Theory d

  1310, Fall, Graduate School of Science, 3
• From 01 Apr. 2022, To 31 Mar. 2023

  Seminar on Probability Theory b

  1308, Fall, Graduate School of Science, 3
• From 01 Apr. 2022, To 31 Mar. 2023

  ILAS Seminar-E2

  Z002, Spring, Institute for Liberal Arts and Sciences, 2
• From 01 Apr. 2022, To 31 Mar. 2023

  Second Course in Statistics-E2

  N816, Spring, Institute for Liberal Arts and Sciences, 2
• From 01 Apr. 2022, To 31 Mar. 2023

  Seminar on Probability Theory a

  1307, Spring, Graduate School of Science, 3
• From 01 Apr. 2022, To 31 Mar. 2023

  Seminar on Probability Theory c

  1309, Spring, Graduate School of Science, 3
• From Apr. 2019, To Mar. 2020

  Function Theory of a Complex Variable-E2

  Spring, 全学共通科目
• From Apr. 2019, To Mar. 2020

  ILAS Seminar-E2

  Spring, 全学共通科目
• From Apr. 2019, To Mar. 2020

  Mathematical Statistics-E2

  Spring, 全学共通科目
• From Apr. 2019, To Mar. 2020

  Mathematical Statistics-E2

  Fall, 全学共通科目
• From Apr. 2019, To Mar. 2020

  Quest for Mathematics I-E2

  Spring, 全学共通科目
• From Apr. 2019, To Mar. 2020

  Second Course in Statistics-E2

  Fall, 全学共通科目
• From Apr. 2019, To Mar. 2020

  Seminar on Applied Analysis 1

  Year-long, 情報学研究科
• From Apr. 2019, To Mar. 2020

  Topics in Applied Analysis I

  Fall, 情報学研究科
• From Apr. 2019, To Mar. 2020

  Topics in Nonlinear Analysis A

  Fall, 情報学研究科
• From Apr. 2020, To Mar. 2021

  ILAS Seminar-E2 :Introduction to Probability

  Spring, 全学共通科目
• From Apr. 2020, To Mar. 2021

  Mathematical Statistics-E2

  Spring, 全学共通科目
• From Apr. 2020, To Mar. 2021

  Mathematical Statistics-E2

  Fall, 全学共通科目
• From Apr. 2020, To Mar. 2021

  Second Course in Statistics-E2

  Fall, 全学共通科目
• From Apr. 2020, To Mar. 2021

  Topics in Applied Analysis I

  Fall, 情報学研究科
• From Apr. 2020, To Mar. 2021

  Seminar on Probability Theory a

  Spring, 理学研究科
• From Apr. 2020, To Mar. 2021

  Seminar on Probability Theory b

  Fall, 理学研究科
• From Apr. 2020, To Mar. 2021

  Seminar on Probability Theory c

  Spring, 理学研究科
• From Apr. 2020, To Mar. 2021

  Seminar on Probability Theory d

  Fall, 理学研究科
• From Apr. 2021, To Mar. 2022

  ILAS Seminar-E2 :Introduction to Probability

  Spring, 全学共通科目
• From Apr. 2021, To Mar. 2022

  Mathematical Statistics-E2

  Spring, 全学共通科目
• From Apr. 2021, To Mar. 2022

  Mathematical Statistics-E2

  Fall, 全学共通科目
• From Apr. 2021, To Mar. 2022

  Second Course in Statistics-E2

  Fall, 全学共通科目
• From Apr. 2021, To Mar. 2022

  Seminar on Probability Theory a

  Spring, 理学研究科
• From Apr. 2021, To Mar. 2022

  Seminar on Probability Theory b

  Fall, 理学研究科
• From Apr. 2021, To Mar. 2022

  Seminar on Probability Theory c

  Spring, 理学研究科
• From Apr. 2021, To Mar. 2022

  Seminar on Probability Theory d

  Fall, 理学研究科

Participation in PhD Defense

• Convergence of processes time-changed by Gaussian multiplicative chaos

  OOI TAKUMU, Graduate School of Science, Chief Examiner

  25 Mar. 2024
• Some inequalities between Ahlfors regular conformal dimension and spectral dimensions for resistance forms

  SASAYA KOHEI, Graduate School of Science, Sub-chief Examiner

  23 Mar. 2023