Publications

1. The incompressible Navier–Stokes limit from the discrete-velocity BGK Boltzmann equation, (with Zhongyang Gu, Xin Hu, Pritpal Matharu, Bartosz Protas, Tsuyoshi Yoneda), Nonlinearity (2025).  arXiv:2407.20804 

2. Characterization of Gradient Condition for Asymmetric Partial Exclusion Processes and Their Scaling Limits, (with Patrícia Gonçalves, Kohei Hayashi), ALEA, Lat. Am. J. Probab. Math. Stat. 22, 331–356 (2025). arXiv:2405.15142

3. Topological structures of large-scale interacting systems via uniform functions and forms,（with Kenichi Bannai, Yukio Kametani ）, Forum of Mathematics, Sigma, (2024). arXiv:2009.04699

4. Relationships between two linearizations of the box-ball system : Kerov-Kirillov-Reschetikhin bijection and slot configuration,  (with Hayate Suda, Matteo Mucciconi, Tomohiro Sasamoto), Forum of Mathematics, Sigma,(2024).  arXiv:2301.00132

5. Yang-Baxter maps and independence preserving property, 

 (with Ryosuke Uozumi), Electronic Journal of Probability, (2024),29 1-21. arXiv:2212.00963

6. Dynamics of the box-ball system with random initial conditions via Pitman's transformation, (with D. A. Croydon, T. Kato, and S. Tsujimoto),  Memoirs of the AMS, 283(1398)(2023).  arXiv:1806.02147

7. Bi-infinite solutions for KdV- and Toda-type discrete integrable systems based on path encodings, (with D. A. Croydon, S. Tsujimoto). Math. Phys, Analysis & Geometry. 25(4) (2022). arXiv:2011.00690

8. On the Stationary Solutions of Random Polymer Models and Their Zero-Temperature Limits, (with D. A. Croydon),  J. Stat. Phys. 188(3) (2022).

9. Generalized hydrodynamic limit for the box-ball system, (with D. A. Croydon), Commun. Math. Phys.(2021), 383(1), 427-463.   arXiv:2003.06526

10. Discrete integrable systems and Pitman's transformation, (with D. A. Croydon), Advanced Studies in Pure Mathematics, (2021), 87,381-402.   arXiv:2007.06206

11.  Hydrodynamic limit for a facilitated exclusion process, (with O. Blondel, C. Erignoux and M. Simon), Ann. Inst. H. Poincaré  Probab. Statist, (2020), 56-1, 667-714.  arXiv:1805.09000

12. Dynamics of the ultra-discrete Toda lattice via Pitman's transformation, (with D. A. Croydon and S. Tsujimoto), RIMS Kokyuroku Bessatsu78 (2020), 235-250.    arXiv:1904.13185

13. Duality between box-ball systems of finite box and/or carrier capacity, (with D. A. Croydon), RIMS Kokyuroku Bessatsu 79(2020), 63-107.   arXiv:1905.00189

14. 5/6-Superdiffusion of energy for coupled charged harmonic oscillators in a magnetic field, (with K. Saito and H. Suda),  Commun. Math. Phys. 372-1 (2019), 151-182.  arXiv:1808.01040  published version

15.  Invariant measures for the box-ball system based on stationary Markov chains and periodic Gibbs measures, (with D. A. Croydon), Journal of Mathematical Physics, 60 083301 (2019). arXiv:1905.00186

16.  On the Green-Kubo formula and the gradient condition on currents, Ann. Appl. Probab. 28, No. 5, (2018), 2727-2739. ( draft version : arXiv:1704.03745)

17. Thermal Conductivity for Coupled Charged Harmonic Oscillators with Noise in a Magnetic Field, (with K. Saito), Commun. Math. Phys. 361-3  (2018), 951–995. arXiv:1706.09668 

18.   Heat transport via low-dimensional systems with broken time-reversal symmetry, (with S. Tamaki and K. Saito), Phys. Rev. Lett. 119 (2017), 110602.

19.   Algebraic structure of vector fields in financial diffusion models and its applications,(with Y. Morimoto), Quantitative Finance (2017), 1105-1117.arXiv:1510.02013

20.   A new approach to the characterization of closed forms in the nongradient method,(with Y. Kametani), RIMS Kokyuroku BessatsuB59 (2016), 1-13.

21.   Spectral gap for stochastic energy exchange model with nonuniformly positive rate function,  Ann. Probab.43 (2015), no. 4, 1663–1711.arXiv:1305.4066

22. From normal diffusion to superdiffusion of energy in the evanescent flip noise limit, (with C. Bernardin, P. Gonçalves, M. Jara and M. Simon), J. Stat. Phys.159 (2015), no. 6, 1327–1368.arXiv:1409.6437 

23.   Stochastic energy exchange models with degenerate rate functions, XVIIth International Congress on Mathematical Physics,World Sci. Publ., Hackensack, NJ,(2014),344–350.

24. Macroscopic energy diffusion for a chain of anharmonic oscillators, (with S. Olla), Probab. Theory Relat. Fields157 (2013), no. 3-4, 721–775.arXiv:1109.5297

25. On the spectral gap of the Kac walk and other binary collision processes on d-dimensional lattice, Symmetries, integrable systems and representations, Springer Proc. Math. Stat. 40 Springer, Heidelberg,(2013), 543–560.arXiv:1308.5096

26. Fluctuations in an evolutional model of two-dimensional Young diagrams, (with T. Funaki, M. Sauer and B. Xie), Stochastic Process. Appl.123 (2013), no. 4, 1229–1275.arXiv:1112.2352 

27. Hydrodynamic limit for exclusion processes with velocity, Markov Process. Related Fields17 (2011), no. 3, 391–428.

28. Spectral gap for multi-species exclusion processes, (with Y. Nagahata), J. Stat. Phys.143 (2011), no. 2, 381–398.

29. Hydrodynamic limit for particle systems with degenerate rates without exclusive constraints, ALEA Lat. Am. J. Probab. Math. Stat7(2010), 277–292.arXiv:1008.3769

30.   Hydrodynamic limit for an evolutional model of two-dimensional Young diagrams, (with T. Funaki), Comm. Math. Phys.299 (2010), no. 2, 335–363.arXiv:0909.5482

31.  Hydrodynamic limit for two-species exclusion processes, Stochastic Process. Appl.120 (2010), no. 4, 494–521.arXiv:0910.3994

Preprint

1. Ultra-discretization of Yang-Baxter maps, probability distributions and independence preserving property, (with Hiroki Kondo and

 Sachiko Nakajima). 2025  arXiv:2504.21359

2. Scaling limits of solitons in the box-ball system, (with Stefano Olla and Hayate Suda). 2024 arXiv:2411.14818

3. On Interactions for Large Scale Interacting Systems, (with Kenichi Bannai, Jun Koriki, Hidetada Wachi and Shuji Yamamoto). 2024  arXiv:2410.06778 

4. On Uniform Functions on Configuration Spaces of Large Scale Interacting Systems, (with Kenichi Bannai). 2024 arXiv:2408.12886

5.  Varadhan's decomposition of shift-invariant closed uniform forms for large scale interacting systems on general crystal lattices, (with Kenichi Bannai). 2022  arXiv:2208.14917

6. Detailed balance and invariant measures for systems of locally-defined dynamics, (with D.A. Croydon).  2020 arXiv:2007.06203

7.  Thermal conductivity for stochastic energy exchange models. 2016  arXiv:1611.08866

8. Eigenvalue problem for some special class of anti-triangular matrices, (with H. Ochiai, T. Shirai and T. Tsuboi). 2014  arXiv:1403.6797

Congress Talks

1. XVII International Congress on Mathematical Physics (ICMP2012), Aalborg, DENMARK, 2012

2. XIX International Congress on Mathematical Physics (ICMP2018), Centre Mont-Royal, CANADA, 2018

Lecture Series

1. Intensive course, Kyusyu University, 2018

2. Intensive course, Tokyo Metropolitan University, 2018

3. Fall 2019 Minerva Lectures, Columbia University, U.S.A. 2019

4. Intensive course, Ochanomizu University, 2022

5. Intensive course, Chiba University, 2025

6. Intensive course, GSSI, Italy, 2025

Editorial Activities

1. Associate editor for Probability Theory and Related topics : 2021-

2. Associate editor for Annales de I'Institute Henri Poincare, Probabilites et  Statistiques : 2021-

International Guests (With Stays Over Ten Days)

2025

• Federico Sau 2025/10/20~2025/11/01 (Universita Degli Studi Di Milano)

• Wai-Kit Lam 2025/06/21-2025/07/20(National Taiwan University)

• Hugo Da Cunha 2025/06/16~2025/08/26 (Université Lyon 1)

• Joao Pedro Mangi 2025/04/27-2025/06/15 (IMPA)

• Jacek Wesolowski 2025/01/31 -2025/02/15 (Warsaw University of Technology)

　 2024

• Stefano Olla 2024/10/18 -2024/11/30 (University Paris Dauphine)

• Chiara Franceschini 2024/09/30 -2024/10/18 (Università di Modena e Reggio Emilia)

• Patricia Goncalves 2024/09/30 -2024/10/11 (Instituto Superior Técnico)