Shuta Nakajima

Associate Professor at Keio University


Education

  • April 2007 - March 2010
    Hamamatsu Kita High School
  • April 2010 - March 2014
    Nagoya University
  • April 2014 - March 2016
    Master in Research Institute for Mathematical Sciences, Kyoto University
  • April 2016 - March 2019
    Ph.D. in Research Institute for Mathematical Sciences, Kyoto University
    Advisor: Ryoki Fukushima

教育

  • 2007年4月 - 2010年3月
    浜松北高等学校
  • 2010年4月 - 2014年3月
    名古屋大学 理学部
  • 2014年4月 - 2016年3月
    京都大学 数理解析研究所 修士課程
  • 2016年4月 - 2019年3月
    京都大学 数理解析研究所 博士課程
    指導教員: 福島竜輝准教授

Academic Position

  • April 2016 - March 2019
    JSPS Research Fellow DC1 at Kyoto University
  • April 2019 - March 2020
    JSPS Research Fellow (Postdoc) at Nagoya University
    Under Nobuo Yoshida
  • April 2020 - March 2022
    Postdoctoral researcher at University of Basel
    Under David Belius
  • April 2022 - August 2025
    Senior Lecturer at Meiji University
  • September 2025 - present
    Associate Professor at Keio University

職歴

  • 2016年4月 - 2019年3月
    京都大学 JSPS特別研究員DC1
  • 2019年4月 - 2020年3月
    名古屋大学 JSPSポスドク研究員
    受入研究員: 吉田伸生教授
  • 2020年4月 - 2022年3月
    バーゼル大学 ポスドク研究員
    採用者: David Belius
  • 2022年4月 - 2025年8月
    明治大学 専任講師
  • 2025年9月 - 現在
    慶應義塾大学 准教授

Awards

2018 Takebe Prize

賞罰

2018年度建部賞

Publications

  1. Lam, Wai-Kit; Nakajima, Shuta. “Moderate deviations in first-passage percolation for bounded weights.” Journal of Mathematical Physics 67 (2026), 073302. doi:10.1063/5.0316577.
  2. Can, Van Hao; Kubota, Naoki; Nakajima, Shuta. “Upper tail large deviation for the one-dimensional frog model.” Probability Theory and Related Fields 194 (2026), 1945–2023. doi:10.1007/s00440-026-01478-w.
  3. Junk, Stefan; Nakajima, Shuta. “Equivalence of fluctuations of discretized SHE and KPZ equations in the subcritical weak disorder regime.” Probability and Mathematical Physics 6 (2025), no. 3, 819–856. doi:10.2140/pmp.2025.6.819.
  4. Can, Van Hao; Kubota, Naoki; Nakajima, Shuta. “Lipschitz-Type Estimate for the Frog Model with Bernoulli Initial Configuration.” Mathematical Physics, Analysis and Geometry 28 (2025), Article 1. doi:10.1007/s11040-024-09497-6.
  5. Can, Van Hao; Nguyen, Van Quyet; Nakajima, Shuta. “Lipschitz continuity of time constants in generalized FPP.” Stochastic Processes and their Applications 175 (2024), 104402. doi:10.1016/j.spa.2024.104402.
  6. Maillard, Antoine; Bandeira, Afonso S.; Belius, David; Dokmanić, Ivan; Nakajima, Shuta. “Injectivity of ReLU networks: perspectives from statistical physics.” Applied and Computational Harmonic Analysis 76 (2024), 101736. doi:10.1016/j.acha.2024.101736.
  7. Cosco, Clément; Nakajima, Shuta; Schweiger, Florian. “Asymptotics of the p-capacity in the critical regime.” J. Convex Anal., to appear.
  8. Cosco, Clément; Nakajima, Shuta. “A variational formula for large deviations in first-passage percolation under tail estimates.” Ann. Appl. Probab. 33 (2023), no. 3, 2103–2135.
  9. Nakajima, Shuta; Sun, Nike. “Sharp threshold sequence and universality for Ising perceptron models.” SODA 2023, 638–674.
  10. E. Bolthausen, S. Nakajima, N. Sun, C. Xu. “Gardner formula for Ising perceptron models at small densities.” COLT 2023, 1787–1911.
  11. Nakajima, Shuta; Nakashima, Makoto. “Fluctuations of two-dimensional stochastic heat equation and KPZ equation in subcritical regime for general initial conditions.” Electron. J. Probab. 28 (2023), Paper No. 1, 38 pp.
  12. Cosco, Clément; Nakajima, Shuta; Nakashima, Makoto. “Law of large numbers and fluctuations in the sub-critical and $L^2$ regions for SHE and KPZ equation in dimension $d \geq 3$.” Stochastic Process. Appl. 151 (2022), 127–173.
  13. Nakajima, Shuta. “Maximal edge-traversal time in First Passage Percolation.” Electron. J. Probab. 27 (2022), Paper No. 19, 32 pp.
  14. David Belius, Jiří Černý, Marius Schmidt, Shuta Nakajima. “Triviality of the geometry of mixed p-spin spherical Hamiltonians with external field.” J. Stat. Phys. 186 (2022), no. 1, Paper No. 12, 34 pp.
  15. Cosco, Clément; Nakajima, Shuta. “Gaussian fluctuations for the directed polymer partition function for $d \geq 3$ and in the whole $L^2$-region.” Ann. Inst. Henri Poincaré Probab. Stat. 57 (2021), no. 2, 872–889.
  16. Nakajima, Shuta. “Divergence of shape fluctuation for general distributions in first-passage percolation.” Ann. Inst. Henri Poincaré Probab. Stat. 56 (2020), no. 2, 782–791.
  17. Nakajima, Shuta. “Divergence of non-random fluctuation in first passage percolation.” Electron. Commun. Probab. 24 (2019), Paper No. 65, 13 pp.
  18. Can, Van Hao; Nakajima, Shuta. “First passage time of the frog model has a sublinear variance.” Electron. J. Probab. 24 (2019), Paper No. 76, 27 pp.
  19. Nakajima, Shuta. “On properties of optimal paths in first-passage percolation.” J. Stat. Phys. 174 (2019), no. 2, 259–275.
  20. Nakajima, Shuta. “Concentration results for directed polymer with unbounded jumps.” ALEA Lat. Am. J. Probab. Math. Stat. 15 (2018), no. 1, 1–20.
  21. Comets, Francis; Fukushima, Ryoki; Nakajima, Shuta; Yoshida, Nobuo. “Limiting results for the free energy of directed polymers in random environment with unbounded jumps.” J. Stat. Phys. 161 (2015), no. 3, 577–597.

出版物

  1. Lam, Wai-Kit; Nakajima, Shuta. 「Moderate deviations in first-passage percolation for bounded weights.」 Journal of Mathematical Physics 67 (2026), 073302. doi:10.1063/5.0316577.
  2. Can, Van Hao; Kubota, Naoki; Nakajima, Shuta. 「Upper tail large deviation for the one-dimensional frog model.」 Probability Theory and Related Fields 194 (2026), 1945–2023. doi:10.1007/s00440-026-01478-w.
  3. Junk, Stefan; Nakajima, Shuta. 「Equivalence of fluctuations of discretized SHE and KPZ equations in the subcritical weak disorder regime」 Probability and Mathematical Physics 6 (2025), no. 3, 819–856. doi:10.2140/pmp.2025.6.819.
  4. Can, Van Hao; Kubota, Naoki; Nakajima, Shuta. 「Lipschitz-Type Estimate for the Frog Model with Bernoulli Initial Configuration」 Mathematical Physics, Analysis and Geometry 28 (2025), Article 1. doi:10.1007/s11040-024-09497-6.
  5. Can, Van Hao; Nguyen, Van Quyet; Nakajima, Shuta. 「Lipschitz continuity of time constants in generalized FPP」 Stochastic Processes and their Applications 175 (2024), 104402. doi:10.1016/j.spa.2024.104402.
  6. Maillard, Antoine; Bandeira, Afonso S.; Belius, David; Dokmanić, Ivan; Nakajima, Shuta. 「Injectivity of ReLU networks: perspectives from statistical physics」 Applied and Computational Harmonic Analysis 76 (2024), 101736. doi:10.1016/j.acha.2024.101736.
  7. Cosco, Clément; Nakajima, Shuta; Schweiger, Florian. 「Asymptotics of the p-capacity in the critical regime」 J. Convex Anal.（掲載予定）.
  8. Cosco, Clément; Nakajima, Shuta. 「A variational formula for large deviations in first-passage percolation under tail estimates」 Ann. Appl. Probab. 33 (2023), no. 3, 2103–2135.
  9. Nakajima, Shuta; Sun, Nike. 「Sharp threshold sequence and universality for Ising perceptron models」 SODA 2023, 638–674.
  10. E. Bolthausen, S. Nakajima, N. Sun, C. Xu. 「Gardner formula for Ising perceptron models at small densities」 COLT 2023, 1787–1911.
  11. Nakajima, Shuta; Nakashima, Makoto. 「Fluctuations of two-dimensional stochastic heat equation and KPZ equation in subcritical regime for general initial conditions」 Electron. J. Probab. 28 (2023), Paper No. 1, 38 pp.
  12. Cosco, Clément; Nakajima, Shuta; Nakashima, Makoto. 「Law of large numbers and fluctuations in the sub-critical and $L^2$ regions for SHE and KPZ equation in dimension $d \geq 3$」 Stochastic Process. Appl. 151 (2022), 127–173.
  13. Nakajima, Shuta. 「Maximal edge-traversal time in First Passage Percolation」 Electron. J. Probab. 27 (2022), Paper No. 19, 32 pp.
  14. David Belius, Jiří Černý, Marius Schmidt, Shuta Nakajima. 「Triviality of the geometry of mixed p-spin spherical Hamiltonians with external field」 J. Stat. Phys. 186 (2022), no. 1, Paper No. 12, 34 pp.
  15. Cosco, Clément; Nakajima, Shuta. 「Gaussian fluctuations for the directed polymer partition function for $d \geq 3$ and in the whole $L^2$-region」 Ann. Inst. Henri Poincaré Probab. Stat. 57 (2021), no. 2, 872–889.
  16. Nakajima, Shuta. 「Divergence of shape fluctuation for general distributions in first-passage percolation」 Ann. Inst. Henri Poincaré Probab. Stat. 56 (2020), no. 2, 782–791.
  17. Nakajima, Shuta. 「Divergence of non-random fluctuation in first passage percolation」 Electron. Commun. Probab. 24 (2019), Paper No. 65, 13 pp.
  18. Can, Van Hao; Nakajima, Shuta. 「First passage time of the frog model has a sublinear variance」 Electron. J. Probab. 24 (2019), Paper No. 76, 27 pp.
  19. Nakajima, Shuta. 「On properties of optimal paths in first-passage percolation」 J. Stat. Phys. 174 (2019), no. 2, 259–275.
  20. Nakajima, Shuta. 「Concentration results for directed polymer with unbounded jumps」 ALEA Lat. Am. J. Probab. Math. Stat. 15 (2018), no. 1, 1–20.
  21. Comets, Francis; Fukushima, Ryoki; Nakajima, Shuta; Yoshida, Nobuo. 「Limiting results for the free energy of directed polymers in random environment with unbounded jumps」 J. Stat. Phys. 161 (2015), no. 3, 577–597.

Invited Talks

Tail estimates in First-passage percolation
October 26–29, 2026
The 24th Symposium "Stochastic Analysis on Large Scale Interacting Systems", Graduate School of Mathematical Sciences, University of Tokyo, Japan
Workshop page
Recent progress on Ising perceptron
April 10–12, 2026
The 3rd NYU Shanghai–Peking–Westlake Probability Conference, Peking University, Beijing, China
Workshop page
Tail estimates in First-passage percolation
March 9–13, 2026
Workshop "Localization, Delocalization, and Diffusion in Disordered Systems", Banff International Research Station (BIRS), Banff, Canada
Maximum of the 2D directed polymer in the subcritical regime and Inhomogeneous Branching Brownian Motion
February 16, 2026
名古屋確率論ワークショップ (Nagoya Probability Workshop), Nagoya University, Nagoya, Japan
Workshop page
Moderate deviations in First-passage percolation for bounded weights
September 8–12, 2025
University POLITEHNICA Bucharest, Bucharest, Romania
Moderate deviations in First-passage percolation for bounded weights
August 25–29, 2025
International Symposium “Stochastic Processes and Complex Systems (SPCS)”, Tohoku University (Sendai, Japan)
Workshop page  Abstract  Slides
Maximum of the 2D directed polymer in the subcritical regime and Inhomogeneous Branching Brownian Motion
June 16–20, 2025
Hokkaido University, Sapporo, Japan
"Maximum of partition functions for 2D directed polymers in subcritical regime", Probability Workshop in Korea 2025, Seoul, Korea, 2025, 1月.
"Sharp thresholds and universality in Ising perceptron models", Kansai Probability Seminar, Kyoto, 2024, 11月.
"Equivalence of fluctuations between SHE and KPZ in weak disorder", Recent developments in Kardar-Parisi-Zhang universality, Yukawa Hall, Japan, 2024, 9月.
"Sharp thresholds and universality in Ising perceptron models", TPW2024, Taiwan, 2024, 6月.
"Upper tail large deviation for the one-dimensional frog model", KIAS APP Seminar, Korea, 2024, 5月.
"On upper tail large deviation rate function for chemical distance in super-critical percolation", Interacting particle systems and SPDEs, BIMSA, Beijing, China, 2024, 3月.
"Upper Tail Large Deviation and Its Application to Maximal Edge-Traversal Time in First-Passage Percolation", IHES seminar, France, 2024, 3月.
"On upper tail large deviation rate function for chemical distance in super-critical percolation", Dauphine-PSL Paris probability seminar, Dauphine-PSL Paris, France, 2024, 3月.
"Equivalence of fluctuations between SHE and KPZ in weak disorder", French Japanese conference, IHES, France, 2024, 3月.
"Equivalence of fluctuations between SHE and KPZ in weak disorder", Random Interacting Systems, Scaling Limits, and Universality, IMS, Singapore, 2023, 12月.
"Leading order of maximal edge-traversal time in First-passage percolation", SPRF, Kyoto, Japan, 2023, 9月.
"On upper tail large deviation rate function for chemical distance in super-critical percolation", Percolation today (online), 2023, 5月.
"First-passage percolationとその周辺", 日本数学会特別講演, Chuo University, Tokyo, Japan, 2023, 3月.
"高次元のKPZ方程式とその周辺", 数理新人セミナー特別講演, Kyushu University, Fukuoka, Japan, 2023, 2月.
"On upper tail large deviation rate function for chemical distance in super-critical percolation", LN-UMN Joint Probability Seminar (online), 2022, 11月.
"A variational formula for large deviations in First-passage percolation under tail estimates", ICTS, Bengaluru, India, 2022, 7月.
"A variational formula for large deviations in First-passage percolation under tail estimates", Zurich University, Zurich, Switzerland, 2022, 2月.
'The fluctuations in the L2 region for the KPZ equation in dimension three and higher', CIRM, Marseille, France, 2021, 9月.
"Triviality of the geometry of mixed p-spin spherical Hamiltonians with external field", 確率解析とその周辺, Online, 2020年, 11月.
"Gaussian Fluctuations in Directed Polymers", Probability Seminar Series, NYU Shanghai, China, 2019, September.
"Divergence of non-random fluctuation in first-passage percolation", The 12th Mathematical Society of Japan, Seasonal Institute (MSJ-SI) Stochastic Analysis, Random Fields and Integrable Probability, Kyushu University, Japan, 2019, August.
"Central limit theorems in directed polymer", Seminar in Probability Theory and Statistics, Basel University, Basel, Switzerland, 2019, June.
"Central limit theorems in directed polymers", Japan Netherlands workshop probabilistic methods in statistical mechanics of random media, Leiden University, Leiden, Netherlands, 2019, June.
"Ergodic property of the number of infinite geodesics in First-passage percolation", Gaussian Free Fields and Related Topics, Kyoto University, Kyoto, Japan, 2018, September.
"The cardinality of infinite geodesics originating from zero in First Passage Percolation", 東京確率論セミナー, 東京大学, 2017年, 5月.
"Maximal edge-traversal time in first passage percolation", 15th workshop on Stochastic Analysis on Large Scale Interacting Systems, Tokyo University, Tokyo, Japan, 2016, November.
"Concentration of first passage percolation", 14th Stochastic Analysis on Large Scale Interacting Systems, Kyoto University, Kyoto, Japan, 2015, October.
"Concentration for first passage percolation", The Third NIMS Summer School in Probability, National Institute for Mathematical Sciences, Daejeon, South Korea, 2015, June.