Updated on 2024/03/05
博士（理学） （ 2012.3 京都大学 ）
polymer model
Branching process
Nagoya University Associate professor
2015.11
University of Tsukuba, Division of Mathematics, Assistant professor Assistant Professor
2012.4 - 2015.11
Country：Japan
Kyoto University Graduate School, Division of Science
- 2012.3
Country： Japan
Kyoto University Faculty of Science
- 2007.3
Country： Japan
日本数学会
日本数学会統計数学分科会確率論 運営委員
2023.4 - 2025.3
Committee type：Academic society
日本数学会 中部支部評議員
2019.4 - 2020.3
Committee type：Academic society
日本数学会賞建部賢弘賞奨励賞
2014.9 日本数学会
Fluctuations of two-dimensional stochastic heat equation and KPZ equation in subcritical regime for general initial conditions Reviewed
Nakajima Shuta, Nakashima Makoto
ELECTRONIC JOURNAL OF PROBABILITY Vol. 28 2023
Law of large numbers and fluctuations in the sub-critical and L2 regions for SHE and KPZ equation in dimension d≥3 Reviewed International coauthorship
Clément, Cosco. Shuta, Nakajima. Makoto Nakashima
Stochastic Processes and their Applications Vol. 151 page： 127 - 173 2022.9
Law of large numbers and fluctuations in the sub-critical and L-2 regions for SHE and KPZ equation in dimension d >= 3
Cosco Clement, Nakajima Shuta, Nakashima Makoto
STOCHASTIC PROCESSES AND THEIR APPLICATIONS Vol. 151 page： 127 - 173 2022.9
THE PERIOD GROUP OF A CHARACTERISTIC FUNCTION Reviewed
Fukushima Ryoki, Nakashima Makoto, Yoshida Nobuo
REAL ANALYSIS EXCHANGE Vol. 47 ( 2 ) page： 323 - 332 2022
Free energy of directed polymers in random environment in 1+1-dimension at high temperature Reviewed
Nakashima Makoto
ELECTRONIC JOURNAL OF PROBABILITY Vol. 24 2019
The free energy of the random walk pinning model
Nakashima Makoto
STOCHASTIC PROCESSES AND THEIR APPLICATIONS Vol. 128 ( 2 ) page： 373-403 2018.2
Branching random walks in random environment and super-Brownian motion in random environment Reviewed
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques Vol. 51 ( 4 ) page： 1251-1289 2015
A remark on the bound for the free energy of directed polymers in random environment in 1+2 dimension Reviewed
Journal of Mathematical Physics Vol. 55 2014
Lower deviations of branching processes in random environment with geometrical offspring distribution, Reviewed
Makoto Nakashima
Stochastic Processes and their Applications Vol. 123 ( 9 ) page： 3560 - 3587 2013.9
Minimal Positions of Branching Random Walks in Random Environment Reviewed
Makoto Nakashima
Journal of Theoretical Probability volume Vol. 26 ( 4 ) page： 1181 - 1217 2012.3
Almost sure central limit theorem for branching random walks in random environment Reviewed
Makoto Nakashima
The Annals of Applied Probability Vol. 21 ( 1 ) page： 351 - 373 2011.2
A Remark on Localization for Branching Random Walks in Random Environment Reviewed International coauthorship
Hadrian Heil, Makoto Nakashima
Electronic Communications in Probability Vol. 16 page： 323 - 336 2011
Branching Random Walks in Random Environment are Diffusive in the Regular Growth Phase Reviewed International coauthorship
Hadrian Heil, Makoto Nakashima, Nobuo Yoshida
Electronic Journal of Probability Vol. 16 page： 1318 - 1340 2011
Central Limit Theorems for Linear Stochastic Evolutions Invited Reviewed
Makoto Nakashima
Journal of Mathematics of Kyoto University Vol. 49 ( 1 ) page： 201 - 224 2009
数理科学 2023年3月号 No.717
白井朋之, 中島誠, 原隆, 白石大典, 田崎晴明, 角田謙吉, 香取眞理, 来嶋秀治, 吉野元（ Role： Contributor , 統計物理学と確率論）
株式会社サイエンス社 2023.3
高次元確率熱方程式とKPZ方程式のL²-領域における摂動 (確率論シンポジウム)
中島 誠
数理解析研究所講究録 ( 2177 ) page： 96 - 103 2021.4
高次元確率熱方程式とKPZ方程式の$L^2$-領域における摂動 (確率論シンポジウム)
中島 誠
数理解析研究所講究録 Vol. 2177 page： 96 - 103 2021.4
Fluctuations of two-dimensional stochastic heat equation and KPZ equation in subcritical regime for general initial conditions
Shuta Nakajima, Makoto Nakashima
2021.3
Two-sided bounds on free energy of directed polymers on strongly recurrent graphs
Naotaka Kajino, Kosei Konishi, Makoto Nakashima
2020.10
Law of large numbers and fluctuations in the sub-critical and $L^2$ regions for SHE and KPZ equation in dimension $d\geq 3$ International coauthorship
Clément Cosco, Shuta Nakajima, Makoto Nakashima
2020.5
Stochastic quantization of the three dimensional polymer measure Invited International coauthorship International conference
Makoto Nakashima
Stochastic Analysis 2023.11.8 Yuzuru Inahama, Hiroshi Kawabi, Seiichiro Kusuoka, Song Liang
1点相互作用をもつシュレディンガー作用素に対応するFeynman-Kacの公式 Invited
中島誠
東京確率論セミナー 2023.6.12
Feynman-Kac formula associated with Schrodinger operator with one point interaction Invited International conference
Makoto Nakashima
Workshop on Probabilistic Methods in Statistical Mechanics of Random Media and Random Fields 2023 2023.1.12 Frank den Hollander, Evgeny Verbitskiy
高分子模型の臨界点近傍での挙動および 1 点と相 互作用をもつ Schr ̈odinger 方程式 Invited
中島誠
京都大学理学研究科数学教室談話会 2022.12.14 京都大学理学研究科数学教室
ランダム媒質中のピニング模型およびディレクティドポリマーの自由エネルギーに関する補足 Invited
中島誠
The 20th Symposium Stochastic Analysis on Large Scale Interacting Systems 2022.12.9
A remark of the free energy for disordered pinning model and directed polymers in random environment Invited International conference
Makoto Nakashima
Open Japanese-German conference on stochastic analysis and applications 2022.9.22 Martin Huesmann, André Schlichting
A remark of the free energy for some disordered systems Invited International conference
Makoto Nakashima
Probability and Analysis on Random Structures and Related Topics 2022.8.9 David Croydon, Ryoki Fukushima, Naotaka Kajino
Gaussian fluctuations of stochastic heat equation and KPZ equation in higher dimension in L22-regime Invited International conference
Makoto Nakashima
42nd conference on Stochastic Processes and their Applications 2022.7.1 Bernoulli Society for Mathematical Statistics and Probability
Gaussian fluctuations of stochastic heat equation and KPZ equation in higher dimension in L^2 regime Invited International coauthorship
Workshop on Probabilistic Methods in Statistical Mechanics of Random Media and Random Fields 2022 2022.1.13 Frank den Hollander, Evgeny Verbitskiy, Tomoyuki Shirai, Shota Osada
高次元確率熱方程式とKPZ方程式の L 2 -領域における解の摂動 Invited
中島誠
The 19th Symposium Stochastic Analysis on Large Scale Interacting Systems 2021.12.9 長田博文, 角田謙吉, 永幡幸生, 福島竜輝, 舟木直久
Gaussian fluctuations of stochastic heat equation and KPZ equation in higher dimension in subcritical regime Invited International conference
Makoto Nakashima
Rigorous Statistical Mechanics and Related Topics 2021.11.19
Fluctuation in L^2-region for stochastic heat equation and KPZ equation in higher dimension Invited
2021.5.21
Fluctuation in L^2-region for stochastic heat equation and KPZ equation in higher dimension
2021.3.15
高次元確率熱方程式と KPZ 方程式の L2-領域における摂動
中島誠
確率論シンポジウム 2020.12.23 桑江一洋
Random pinning model related to directed polymers in random environment Invited International conference
Makoto Nakashima
Workshop on Probabilistic Methods in Statistical Mechanics of Random Media and Random Fields 2019.5.28 Frank den Hollander, Evgeny Verbitskiy, Tomoyuki Shirai
Free energy of directed polymers in random environment Invited International conference
Makoto Nakashima
The First China-Japan-Korea Probability Workshop 2019.5.11 Zhen-Qing Chen, Panki Kim, Takashi Kumagai, and Zhi-Ming Ma
Free energy of directed polymers in random environment Invited International conference
Makoto Nakashima
Okayama Workshop on Stochastic Analysis 2019 2019.2.6 Seiichiro Kusuoka
Free energy of directed polymers in random environment Invited International conference
Makoto Nakashima
Gaussian Free Fields and Related Topics 2018.9.20 Naotaka Kajino, Takashi Kumagai, Daisuke Shiraishi
Free energy of directed polymers in random environment in 1 + 1 dimension Invited International conference
Makoto Nakashima
Stochastic partial differential equations and related topics 2018.7.27
Analysis, geometry and their interplays on fractals and stochastic processes on them
Grant number：22H01128 2022.4 - 2027.3
Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
Authorship：Coinvestigator(s)
Grant number：22K03351 2022.4 - 2027.3
科学研究費助成事業 基盤研究(C)
中島 誠
Authorship：Principal investigator
Grant amount：\3900000 （ Direct Cost: \3000000 、 Indirect Cost：\900000 ）
ランダム媒中のディレクティドポリマー(DPRE) の1次元における超拡散性(媒質の影響によりブラウン運動に比べて遠くへいくこと)の証明, および確率熱方程式(SHE), KPZ方程式に対してその解の摂動の解析を行う. 超拡散性の証明のために自由エネルギーの解析を行い, その摂動係数と呼ばれる指数を求める. SHEおよびKPZ方程式の解の摂動はあるパラメータの領域においては中心極限定理が成り立つことが知られており, その領域の外における摂動に対する研究を行う.
Analysis and geometry of fractals and stochastic processes on them from field-transverse viewpoints
Grant number：18H01123 2018.4 - 2022.3
Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
Authorship：Coinvestigator(s)
Analysis of statistical mechanical models evolving in random media
Grant number：18K13423 2018.4 - 2022.3
Grant-in-Aid for Early-Career Scientists
Authorship：Principal investigator
Grant amount：\4160000 （ Direct Cost: \3200000 、 Indirect Cost：\960000 ）
Analysis of branching process with interacting particle systems
Grant number：26800051 2014.4 - 2018.3
Nakashima Makoto
Authorship：Principal investigator
Grant amount：\2990000 （ Direct Cost: \2300000 、 Indirect Cost：\690000 ）
Asymptotics of logarithms of the total number of branching random walks in random environment are controlled by the free energy of directed polymers in random environment.
We gave estimates of free energies for directed polymers in random environment in 1 and 2 dimensions.
Also, we study the random walk pinning model to analyze the critical points of directed polymers in random environment in higher dimension. We found that two critical points coincide with each other and we proved the central limit theorem and invariance principle in the subcritical phase for dimension d\geq 3.
個体間に強い相互作用を持つ分枝過程の解析
2014.4 - 2017.3
科学研究費補助金 若手研究(B)
Authorship：Principal investigator
Phase transition in stochastic models and its analysis near critical point
2012.8 - 2014.3
Grant-in-Aid for Scientific Research
Authorship：Principal investigator
数学特別講義3(確率論)
2022.12 （Kyoto University）
Level：Postgraduate Country：Japan
KPZ方程式は特異なSPDEであり, 通常の意味では解が定義できないことがよく知られている. しかし1次元においては97年のBertini-GiacominによるCole-Hopf変換による解の意味づけ, 2013年のHairerによる正則構造理論を用いた解の構成など様々な手法によってSPDEの意味づけと解がなされた.
一方で2次元以上の場合にはまだ解の意味づけには至っていない. この講義ではBertini-Giacominの手法を高次元に適用する解の意味づけに関する近年の取り組みとその結果について述べた後, それらで用いられた手法の紹介を行う.
確率微分方程式
2020.6 - 2020.7 （Nara Women's University）
Level：Postgraduate
Role(s)：Planning, management, etc.
中島誠 2020.9
