Akira Sakaiiβˆδ@“Nj

(ResearchGate, researchmap, Visionary Scientists)

Professor in Mathematics

Faculty of Science

Hokkaido University

 

Contents

I. Research interest

II. Research papers

III. Scientific talks

IV. Organizing scientific meetings

V. Teaching

VI. Curriculum vitae

 

Last updated on September 16, 2025.

 

 

                               I.          Research interesti“ϊ–{Œκ”Ε‚Ν‚±‚Ώ‚ηj

 

To rigorously prove various important statistical-physics phenomena.  They include phase transitions and critical behavior, associated limit theorems, and convergence to equilibrium measures and its application to combinatorial optimization.  The mathematical models I have been interested in are

 

·      Ising models (for magnets) and stochastic cellular automata,

·      ƒΣ4 model (in lattice scalar-field theory),

·      self-avoiding walk (for linear polymers),

·      lattice trees and lattice animals (for branched polymers),

·      percolation (for random media),

·      oriented percolation and the contact process (for the spread of an infectious disease),

·      random walk with reinforcement.

 

 

                           II.          Research papers

 

1.            Y. Kamijima and A. Sakai.  Mean-field behavior of the quantum Ising susceptibility and a new lace expansion for the classical Ising model.  Math. Phys. Anal. Geom. 28 (2025): Article 29 (the full-text view-only version).  arXiv:2501.06592.

2.            Akira Sakai.  Hugo Duminil-CopinŽ‚̋ƐΡ.  ”Šw (Sugaku) 76 (2024):48–60.

3.            N. Kawamoto and A. Sakai.  Spread-out limit of the critical points for lattice trees and lattice animals in dimensions d ˃ 8.  Comb. Probab. Comput., 33 (2024): 238–269.  arXiv:2205.09451.

4.            B.H. Fukushima-Kimura, N. Kawamoto, E. Noda and A. Sakai.  Mathematical aspects of the digital annealerfs simulated annealing algorithm.  J. Stat. Phys., 190 (2023): Article 190.  arXiv:2303.08392.

5.            Y. Kamijima and A. Sakai.  Stability of the phase transition and critical behavior of the Ising model against quantum perturbation.  RIMS Kokyuroku, 2246 (2023): Article 2.

6.            B.H. Fukushima-Kimura, S. Handa, K. Kamakura, Y. Kamijima, K. Kawamura and A. Sakai.  Mixing time and simulated annealing for the stochastic cellular automata.  J. Stat. Phys., 190 (2023): Article 79.  arXiv:2007.11287.

7.            B.H. Fukushima-Kimura, Y. Kamijima, K. Kawamura and A. Sakai.  Stochastic optimization: Glauber dynamics versus stochastic cellular automata.  Transactions of the Institute of Systems, Control and Information Engineers 36 (2023): 9–16.  arXiv:2211.06809.

8.            Akira Sakai.  ƒp[ƒRƒŒ[ƒVƒ‡ƒ“‚̐”— 2020.  ”Šw (Sugaku) 74 (2022): 253–279.

9.            Akira Sakai.  Correct bounds on the Ising lace-expansion coefficients.  Commun. Math. Phys., 392 (2022): 783–823 (the full-text view-only version).  arXiv:2003.09856.

10.        B.H. Fukushima-Kimura, Y. Kamijima, K. Kawamura and A. Sakai.  Stochastic optimization via parallel dynamics: rigorous results and simulations.  Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications 2022 (2022): 65–71.

11.        B.H. Fukushima-Kimura, A. Sakai, H. Toyokawa and Y. Ueda.  Stability of energy landscape for Ising models.  Physica A, 583 (2021): 126208.  arXiv:2105.00449.

12.        K. Yamamoto, K. Kawamura, K. Ando, N. Mertig, T. Takemoto, M. Yamaoka, H. Teramoto, A. Sakai, S. Takamaeda-Yamazaki and M. Motomura.  STATICA: a 512-spin 0.25M-weight annealing processor with an all-spin-updates-at-once architecture for combinatorial optimization with complete spin-spin interactions.  IEEE Journal of Solid-State Circuits, 56 (2021): 165–178.

13.        K. Yamamoto, K. Ando, N. Mertig, T. Takemoto, M. Yamaoka, H. Teramoto, A. Sakai, S. Takamaeda-Yamazaki and M. Motomura.  7.3 STATICA: a 512-spin 0.25M-weight full-digital annealing processor with a near-memory all-spin-updates-at-once architecture for combinatorial optimization with complete spin-spin interactions.  2020 IEEE International Solid-State Circuits Conference.

14.        Akira Sakai.  Crossover phenomena in the critical behavior for long-range models with power-law couplings.  RIMS Kokyuroku Bessatsu, B79 (2020): 51–62.  arXiv:1812.10275.

15.        S. Handa, Y. Kamijima and A. Sakai.  A survey on the lace expansion for the nearest-neighbor models on the BCC lattice.  Taiwanese J. Math., 24 (2020): 723–784.  arXiv:1712.05573.

16.        S. Handa, K. Kamakura, Y. Kamijima and A. Sakai.  Finding optimal solutions by stochastic cellular automata.  arXiv:1906.06645.

17.        L.-C. Chen and A. Sakai.  Critical two-point function for long-range models with power-law couplings: The marginal case for d ³ dc.  Commun. Math. Phys., 372 (2019): 543–572 (the full-text view-only version).  arXiv:1808.06789.

18.        S. Handa, M. Heydenreich and A. Sakai.  Mean-field bound on the 1-arm exponent for Ising ferromagnets in high dimensions.  A chapter in Sojourns in Probability and Statistical Physics - I (V. Sidoravicius ed., Springer, 2019).  arXiv:1612.08809.

19.        A. Sakai and G. Slade.  Spatial moments for high-dimensional critical contact process, oriented percolation and lattice trees.  Electron. J. Probab., 24 (2019): no. 65, 1–18.  arXiv:1810.04011.

20.        Akira Sakai.  Hyperscaling for oriented percolation in 1+1 space-time dimensions.  J. Stat. Phys., 171 (2018): 462–469 (the full-text view-only version).  arXiv:1709.08291.

21.        T. Arae, S. Isai, A. Sakai, K. Mineta, M. Yokota-Hirai, Y. Suzuki, S. Kanaya, J. Yamaguchi, S. Naito and Y. Chiba.  Coordinated regulations of mRNA synthesis and decay during cold acclimation in arabidopsis cells.  Plant Cell Physiol., 58 (2017): 1090–1102.

22.        Y. Chino and A. Sakai.  The quenched critical point for self-avoiding walk on random conductors.  J. Stat. Phys., 163 (2016): 754–764.  arXiv:1508.01262.

23.        Akira Sakai.  Application of the lace expansion to the ƒΣ4 model.  Commun. Math. Phys., 336 (2015): 619–648.  arXiv:1403.5714.

24.        L.-C. Chen and A. Sakai.  Critical two-point functions for long-range statistical-mechanical models in high dimensions.  Ann. Probab., 43 (2015): 639–681.  arXiv:1204.1180.

25.        L.-C. Chen and A. Sakai.  Asymptotic behavior of the gyration radius for long-range self-avoiding walk and long-range oriented percolation.  Ann. Probab., 39 (2011): 507–548.  arXiv:1002.0875.

26.        Akira Sakai.  Large-time asymptotics of the gyration radius for long-range statistical-mechanical models.  RIMS Kokyuroku Bessatsu, B21 (2011): 53–62.  arXiv:0912.5117.

27.        R. van der Hofstad and A. Sakai.  Convergence of the critical finite-range contact process to super-Brownian motion above the upper critical dimension: The higher-point functions.  Electron. J. Probab., 15 (2010): no. 27, 801–894.  arXiv:0809.1712.

28.        L.-C. Chen and A. Sakai.  Critical behavior and the limit distribution for long-range oriented percolation. II: Spatial correlation.  Probab. Theory Relat. Fields, 145 (2009): 435–458.  arXiv:0804.2039.

29.        Akira Sakai.  Applications of the lace expansion to statistical-mechanical models.  A chapter in Analysis and Stochastics of Growth Processes and Interface Models (P. Mörters et al. eds., Oxford University Press, 2008).

30.        M. Heydenreich, R. van der Hofstad and A. Sakai.  Mean-field behavior for long- and finite range Ising model, percolation and self-avoiding walk.  J. Stat. Phys., 132 (2008): 1001–1049.  arXiv:0712.0312.

31.        L.-C. Chen and A. Sakai.  Critical behavior and the limit distribution for long-range oriented percolation. I.   Probab. Theory Relat. Fields, 142 (2008): 151–188.  arXiv:0703455.

32.        Akira Sakai.  Diagrammatic bounds on the lace-expansion coefficients for oriented percolation.  arXiv:0708.2897.

33.        M. Holmes and A. Sakai.  Senile reinforced random walks.  Stoch. Proc. Appl., 117 (2007): 1519–1539.

34.        Akira Sakai.  Lace expansion for the Ising model.  Commun. Math. Phys., 272 (2007): 283–344.  arXiv:math-ph/0510093.

35.        R. van der Hofstad and A. Sakai.  Critical points for spread-out self-avoiding walk, percolation and the contact process above the upper critical dimensions.  Probab. Theory Relat. Fields, 132 (2005): 438–470.  arXiv:math/0402050.

36.        Akira Sakai.  Mean-field behavior for the survival probability and the percolation point-to-surface connectivity.  J. Stat. Phys., 117 (2004): 111–130.

37.        R. van der Hofstad and A. Sakai.  Gaussian scaling for the critical spread-out contact process above the upper critical dimension.  Electron. J. Probab., 9 (2004): no. 24, 710–769.  arXiv:math/0402049.

38.        M. Holmes, A.A. Járai, A. Sakai and G. Slade.  High-dimensional graphical networks of self-avoiding walks.  Canad. J. Math., 56 (2004): 77–114.

39.        Akira Sakai.  Hyperscaling inequalities for the contact process and oriented percolation.  J. Stat. Phys., 106 (2002): 201–211.

40.        Akira Sakai.  Mean-field critical behavior for the contact process.  J. Stat. Phys., 104 (2001): 111–143.

 

 

                       III.          Scientific talks

 

Year 2025

1.       TBA.

·     Kansai Probability Seminar (???). Kyoto University, Japan.

·     Probability Seminar (???). Tohoku University, Japan.

2.       Critical points for various spread-out statistical-mechanics models in high dimensions.

·     The 3rd Taiwan-Japan Joint Workshop on Applied Mathematics (May 1–2). Hokkaido University, Japan.

 

Year 2024

1.       The lace expansion in the past, present and future [YouTube].

·     Math Colloquia (October 31). Seoul National University, South Korea.

2.       Mathematical foundation of ground-state search MCMC methods.

·     Taiwan Probability Workshop 2024 (June 3–7). Institute of Mathematics, Academia Sinica, Taiwan.

·     Forest Workshop 2024 (March 29–31). TKP Garden City Premium Sapporo Odori, Japan.

3.       Mathematical foundation of various MCMC methods [YouTube].

·     French Japanese Conference on Probability & Interactions (March 6–8). IHES, France.

 

Year 2023

1.       Mathematical foundation of various MCMC methods.

·     Mathematics of Random Systems Summer School 2023 (September 11–15). RIMS, Kyoto University, Japan.

2.       Stability of the critical behavior of the Ising model against quantum perturbation.

·     Workshop on Probabilistic Methods in Statistical Mechanics of Random Media and Random Fields 2023 (January 9–13). Kyushu University, Japan.

 

Year 2022

1.       Stability of the critical behavior of the Ising model against quantum perturbation.

·     Tokyo Probability Seminar (December 26). Keio University, Japan.

2.       Stability of the phase transition and critical behavior of the Ising model against quantum perturbation.

·     Probability Symposium (December 19–22). RIMS, Kyoto University, Japan.

3.       Spread-out limit of the critical points for various statistical-mechanics models.

·     Probability and Analysis on Random Structures and Related Topics (August 8–10). RIMS, Kyoto University, Japan.

4.       Mixing time and simulated annealing for the stochastic cellular automata, and beyond.

·     Workshop on Probabilistic Methods in Statistical Mechanics of Random Media and Random Fields 2022 (January 11–14). Kyushu University, Japan.

 

Year 2021

1.       Mixing time and simulated annealing for the stochastic cellular automata, and beyond.

·     The Annual Probability Symposium (December 14–17). Kyoto University, Japan.

2.       Stochastic optimization via parallel dynamics: rigorous  results and simulations.

·     The 53rd ISCIE International Symposium on Stochastic Systems Theory and Its Applications (October 30–31). Ritsumeikan University, Japan.

 

Previous years

 

 

                        IV.          Organizing scientific meetings

 

Year 2025

·          The RIMS Workshop gRigorous Statistical Mechanics and Related Topics VIh (November 10–13, 2025). RIMS, Kyoto University, Japan.

·          The 18th HU-SNU Joint Symposium on Mathematics (October 31, 2025). Science Bldg 3-205 & 4-501, Hokkaido University, Japan.

·          Far East Probability Workshop 2025 (June 16–20, 2025). Hokkaido University, Japan.

·          Hokkaido Math-Sci Seminar (February 21, 2025). Hokkaido University, Japan.

 

Year 2024 & before

·          ”—˜AŒg„iŽΊƒCƒxƒ“ƒguŽΠ‰ο‚ōvŒ£‚·‚鐔Šwvi—Šw‰@E—Šw•”j (December 5, 2024). Hokkaido University, Japan.

·          The RIMS Workshop gRigorous Statistical Mechanics and Related Topics Vh (November 11–14, 2024). RIMS, Kyoto University, Japan.

·          The 17th SNU-HU Joint Symposium on Mathematics (November 1, 2024). Seoul National University, South Korea.

·          2024 Open Japanese-German Conference on Stochastic Analysis (September 9–13, 2024). Hokkaido University, Japan.

·          ”—˜AŒg„iŽΊƒCƒxƒ“ƒgu•Ο‰»‚πŽσ‚―“ό‚κ‚ιŠν|Mac OS X‚Μ’aΆ‚©‚ηiPhone‚ΜŒ΄•—Œi‚ցvi—Šw‰@E—Šw•”j (July 12, 2024). Hokkaido University, Japan.

·          Hokkaido Math-Sci Seminar (February 14, 2024). Hokkaido University, Japan.

·          The IMS Program gRandom Interacting Systems, Scaling Limits, and Universalityh (December 4–22, 2023). IMS, National University of Singapore, Singapore.

·          The 16th HU-SNU Joint Symposium on Mathematics (November 11, 2023). Hokkaido University, Japan.

·          One-day Workshop on Mathematical Analysis (July 11, 2023). Hokkaido University, Japan.

·          ”—˜AŒg„iŽΊƒCƒxƒ“ƒguŽΠ‰ο‚ōvŒ£‚·‚鐔Šwv (December 2, 2022). Hokkaido University, Japan.

·          The RIMS Workshop gRigorous Statistical Mechanics and Related Topics IVh (November 15–18, 2022). RIMS, Kyoto University, Japan.

·          Pacific Workshop on Probability and Statistical Physics (December 9–11, 2021). PIMS, University of British Columbia, Canada.

·          The RIMS Workshop gRigorous Statistical Mechanics and Related Topics IIIh (November 16–19, 2021). RIMS, Kyoto University, Japan.

·          The 10th World Congress in Probability and Statistics (July 19–23, 2021). Seoul National University, South Korea.

·          The RIMS Workshop gRigorous Statistical Mechanics and Related Topics IIh (November 24–27, 2020). RIMS, Kyoto University, Japan.

·          The RIMS Workshop gRigorous Statistical Mechanics and Related Topicsh (November 18–21, 2019). RIMS, Kyoto University, Japan.

·          The 1-day workshop gRecent Progress in Probability Theory and Its Applicationsh (July 28, 2017). Hokkaido University, Japan.

·          2017 Spring Probability Workshop (March 6–8, 2017). Academia Sinica, Taiwan.

·          The 2nd workshop on Universality and Scaling Limits in Probability and Statistical Mechanics (August 5–9, 2013). Hokkaido University, Japan.

·          International Workshop on Potential Theory (February 4, 2013). Hokkaido University, Japan.

·          The RIMS workshop gApplications of Renormalization Group Methods in Mathematical Sciencesh (September 12–14, 2011). Kyoto University, Japan.

·          The SPA Satellite workshop gUniversality and Scaling Limits in Probability and Statistical Mechanicsh (August 30–September 3, 2010). Hokkaido University, Japan.

 

 

                            V.          Teaching (April 2025 – February 2026)

 

2nd semester

Monday

Tuesday

Wednesday

Thursday

Friday

8:45 – 10:15

N.A.

N.A.

N.A.

N.A.

‰πΝŠwF

10:30 – 12:00

N.A.

N.A.

N.A.

SAW on RC

N.A.

13:00 – 14:30

N.A.

N.A.

”χ•ͺΟ•ͺŠwII

G.S.

G.S.

14:45 – 16:15

N.A.

N.A.

N.A.

G.S.{”Šwu“Η

G.S.

16:30 – 18:00

N.A.

N.A.

Q-Ising lace

F.M.

G.S.

18:15 – 19:30

N.A.

N.A.

Q-Ising lace

F.M.

O.H.

          (Research Meetings; Lectures; Group Seminars; Faculty Meetings; Office Hour; Not Available )

 

1.       Research meetings (Wednesdays 16:30–19:30, Thursdays 10:30–12:00)

2.       Lectures

·          ”χ•ͺΟ•ͺŠwII; WeBWorK (Wednesdays 13:00–14:30) @ Multimedia Education Bldg ????

·          ‰πΝŠwF (Fridays 8:45–10:15) @ Science Bldg 3-309

·          ”Šwu“Η (???days ??:??–??:??) @ Science Bldg 4-509

3.       Group Seminars @ Science Bldg 4-509

·          M2 seminar (‘ˆδ) on Hyperscaling for the 1-dimensional contact process in an evolving environment (???days ??:??–??:??)

·          M2 seminar (’|“ΰ) on Nonintersection probability of random walks in high dimensions (???days ??:??–??:??)

·          M2 seminar (‹ίœA) on The 1-arm exponent for percolation & the Ising model in high dimensions (???days ??:??–??:??)

·          M2 seminar (‰Œ©) on Sufficient condition for the mean-field behavior of oriented percolation (???days ??:??–??:??)

·          B4 seminar (–{“c) on Percolation (???days ??:??–??:??)

·          B4 seminar (ŽR–{) on Random walk and stochastic analysis (???days ??:??–??:??)

 

 

1st semester

Monday

Tuesday

Wednesday

Thursday

Friday

8:45 – 10:15

N.A.

‰ΘE‹Z‚̐’ŠE

N.A.

N.A.

Šm—¦E“Œv“ό–ε

10:30 – 12:00

N.A.

N.A.

N.A.

SAW on RC

N.A.

13:00 – 14:30

N.A.

G.S.

”—‰ΘŠwŠTΰ

G.S.

N.A.

14:45 – 16:15

N.A.

G.S.

G.S.

G.S.{”Šwu“Η

”χ•ͺΟ•ͺŠwI

16:30 – 18:30

N.A.

G.S.

Q-Ising lace

F.M.

O.H.

          (Research Meetings; Lectures; Group Seminars; Faculty Meetings; Office Hour; Not Available )

 

1.       Research meetings (Wednesdays 16:30–18:30, Thursdays 10:30–12:00)

2.       Lectures

·          ‰ΘŠwE‹Zp‚̐’ŠEF”Šw‚Μ‚½‚Μ‚΅‚έ (Tuesdays 8:45–10:15) @ Multimedia Education Bldg E205

·          ”—‰ΘŠwŠTΰ (Wednesdays 13:00–14:30) @ Science Bldg 3-202

·          Šm—¦E“Œv“ό–ε (Fridays 8:45–10:15) @ Science Bldg 3-309

·          ”χ•ͺΟ•ͺŠwI; WeBWorK (Fridays 14:45–16:15) @ Multimedia Education Bldg E201

·          ”Šwu“Η (Thursdays 15:20–16:20) @ Science Bldg 4-509

3.       Group Seminars @ Science Bldg 4-509

·          M2 seminar (‘ˆδ) on Hyperscaling for the 1-dimensional contact process (Tuesdays 13:00–14:00)

·          M2 seminar (‹ίœA) on The 1-arm exponent for percolation & the Ising model in high dimensions (Tuesdays 14:10–15:10)

·          M2 seminar (’|“ΰ) on Intersection probability of random walks (Tuesdays 15:20–16:20)

·          B4 seminar (ŽR–{) on Random walk and stochastic analysis (Tuesdays 16:30–17:30)

·          M2 seminar (‰Œ©) on Phase transition & critical behavior of oriented percolation (Thursdays 13:00–14:00)

·          B4 seminar (–{“c) on Percolation (Thursdays 14:10–15:10)

·          HSI seminar (Huang) on Markov Chains and Mixing Times (Wednesdays 14:45–16:15 @ 4-401)

 

 

                        VI.          Curriculum vitae

 

·     February 2020 – present

Professor in Mathematics, Faculty of Science, Hokkaido University, Japan.

Ø  Head of the Department (April 2024 – March 2025)

Ø  Vice head of the Department (April 2023 – March 2024)

Ø  Department head of the Academic Affairs Committee (April 2022 – March 2023)

 

·     March 2020 – present

Associate editor of Mathematical Physics, Analysis and Geometry.

 

·     Excellent Teachers: 2023, 2022, 2021, 2018, 2015, 2012, 2011

The Hokkaido University Presidentfs Award for Teaching Excellence in 2013 and in 2012.

 

·     August 2020 – October 2023

Associate editor of Taiwanese Journal of Mathematics.

 

·     September 2015 – August 2019

Councilor of the Bernoulli Society.

 

·     April 2011 – January 2020

Associate professor in Mathematics, Faculty of Science, Hokkaido University, Japan.

 

·     March 2008 – March 2011

Tenure-track assistant professor of L-Station, Hokkaido University, Japan.

 

·     April 2006 – February 2008

Lecturer in Probability of the Department of Mathematical Sciences, the University of Bath, UK.

 

·     April 2004 – March 2006

Postdoctoral researcher of Wiskunde en Informatica, Technische Universiteit Eindhoven (TU/e), the Netherlands.

 

·     January 2003 – March 2004

Postdoctoral researcher of the Interacting Stochastic Systems (ISS) group, EURANDOM, the Netherlands.

 

·     January 2001 – December 2002

Postdoctoral researcher of the Department of Mathematics, the University of British Columbia, Canada.

 

·     April 1996 – December 2000

Ph.D. study in Applied Physics, Tokyo Institute of Technology, Japan.

Awarded Ph.D. for the thesis gAnalyses of the Critical Behavior for the Contact Process based on a Percolation Structureh supervised by Takashi Hara.

 

·     April 1994 – March 1996

Master study in Applied Physics, Tokyo Institute of Technology, Japan.

Awarded M.Sc. for the thesis gApproach to Fractal Growth Phenomenah supervised by Takashi Hara.

 

·     April 1990 – March 1994

Undergraduate study in Applied Physics, Tokyo Institute of Technology, Japan.

Awarded B.Sc. for the thesis gRecurrent in the Plane, Transient in Spaceh supervised by Kohei Uchiyama.