Akira Sakai

(ResearchGate, researchmap, Visionary Scientists)

 

Professor in Mathematics

Faculty of Science

Hokkaido University

North 10, West 8, Kita-ku, Sapporo

Hokkaido 060-0810

JAPAN

 

Contents

I. Fields of interest

II. Research papers

III. Scientific talks

IV. Organizing scientific meetings

V. Teaching

VI. Curriculum vitae

 

Updated: June 16, 2020.

 

 

                               I.          Fields of interest（日本語版はこちら）

 

My major research field is mathematical physics (probability and statistical mechanics). The topics I have been most fascinated with are phase transitions and critical phenomena, as well as associated scaling limits. For example, the Ising model, a statistical-mechanical model of ferromagnetism, is known to take on positive spontaneous magnetization as soon as the temperature of the system is turned down below the critical point. Various other observables also exhibit singular behavior around the critical point, due to cooperation of infinitely many interacting variables. To fully understand such phenomena, it would require development of a theory beyond the standard probability theory. This is a challenging and intriguing problem, towards which I would love to make even a tiny contribution.

 

The mathematical models I have been studying are

·      the Ising model (for magnets),

·      the φ4 model (in lattice scalar-field theory),

·      self-avoiding walk (for linear polymers),

·      lattice trees (for branched polymers),

·      percolation (for random media),

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

·      random walk with reinforcement.

 

 

                           II.          Research papers

 

1.            Akira Sakai.  Percolation 2020（パーコレーションの数理2020）.  Submitted.

 

2.            Akira Sakai.  Correct bounds on the Ising lace-expansion coefficients.  Submitted.  arXiv:2003.09856.

 

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

 

4.            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.

 

5.            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.

 

6.            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.

 

7.            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.

 

8.            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.

 

9.            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.

 

10.        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.

 

11.        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.

 

12.        Akira Sakai.  Application of the lace expansion to the φ4 model.  Commun. Math. Phys. 336 (2015): 619–648.  arXiv:1403.5714.

 

13.        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.

 

14.        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.

 

15.        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.

 

16.        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.

 

17.        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.

 

18.        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).

 

19.        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.

 

20.        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.

 

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

 

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

 

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

 

24.        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.

 

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

 

26.        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.

 

27.        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.

 

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

 

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

 

 

                       III.          Scientific talks

 

Year 2020

 

1.       May 20–22, NCTS, Taiwan.

2.       June 15–19, IHES, France.

3.       Fall, City University of Hong Kong, China.

4.       Fall, Sun Yat-sen University, Guangzhou, China.

 

Year 2019

 

1.       Finding optimal solutions by stochastic cellular automata.

·     7th Wellington Workshop in Probability and Mathematical Statistics (December 5–7). Wellington, New Zealand.

·     Workshop on Probabilistic Methods in Statistical Mechanics of Random Media and Random Fields (May 27–31). Universiteit Leiden, the Netherlands.

·     AIMaP 1-day Workshop (March 26). RIES, Hokkaido University, Japan.

 

2.       Critical two-point function for long-range models with power-law couplings: The marginal case for d ³ dc.

·     The 12th MSJ-SI “Stochastic Analysis, Random Fields and Integrable Probability” (July 31–August 9). Kyushu University, Japan.

·     Seminar in Statistics (January 16). The University of Auckland, New Zealand.

 

Year 2018

 

1.       Critical two-point function for long-range models with power-law couplings: The marginal case for d ³ dc.

·     17th International Symposium “Stochastic Analysis on Large-scale Interacting Systems”  (November 5–8). RIMS, Kyoto University, Japan.

·     High-dimensional Critical Phenomena in Random Environments (September 24–26). The University of Bristol, UK.

·     2018 Spring Probability Workshop (June 4–8). Academia Sinica, Taiwan.

 

2.       Hyperscaling for oriented percolation in 1+1 space-time dimensions.

·     Rikkyo Math Phys Seminar (May 23). Rikkyo University, Japan

·     NUS Probability Seminar (February 12). National University of Singapore, Singapore.

 

Year 2017

 

1.       Hyperscaling for oriented percolation in 1+1 space-time dimensions.

·     NTU Math Colloquium (November 27). National Taiwan University, Taiwan.

 

2.       Recent progress in researches on phase transitions and critical behavior for Ising ferromagnets（強磁性イジング模型の相転移・臨界現象に関する研究の最近の動向）.

·     MSJ Fall Meeting (September 11–14). Yamagata University, Japan.

 

3.       Critical behavior for oriented percolation: From a mathematically rigorous standpoint.

·     Summer School in Mathematical Physics (August 25–27). The University of Tokyo, Japan.

 

4.       The lace expansion for self-avoiding walk and percolation on the BCC lattice.

·     Seminar on Probability (July 18). Osaka University, Japan.

 

5.       Mean-field bound on the 1-arm exponent for high-dimensional Ising ferromagnets.

·     Physical and Mathematical Approaches to Interacting Particle Systems – In Honer of 70th Birthday of Herbert Spohn (January 11–12). Tokyo Institute of Technology, Japan.

 

Previous years

 

 

                        IV.          Organizing scientific meetings

 

1.            The 3rd workshop on Universality and Scaling Limits in Probability and Statistical Mechanics (Planned in 2021). Hokkaido University, Japan.

 

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

 

3.            The RIMS Workshop “Rigorous Statistical Mechanics and Related Topics II” (November 24–27, 2020). RIMS, Kyoto University, Japan.

 

4.            The RIMS Workshop “Rigorous Statistical Mechanics and Related Topics” (November 18–21, 2019). RIMS, Kyoto University, Japan.

 

5.            The 1-day workshop “Recent Progress in Probability Theory and Its Applications” (July 28, 2017). Hokkaido University, Japan.

 

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

 

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

 

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

 

9.            The RIMS workshop “Applications of Renormalization Group Methods in Mathematical Sciences” (September 12–14, 2011). Kyoto University, Japan.

 

10.        The SPA Satellite workshop “Universality and Scaling Limits in Probability and Statistical Mechanics” (August 30–September 3, 2010). Hokkaido University, Japan.

 

 

                            V.          Teaching (April 2020 – February 2021)

 

1st semester

Monday

Tuesday

Wednesday

Thursday

Friday

8:45 – 10:15

N.A.

Science & Tech

N.A.

N.A.

Explore B-Math

10:30 – 12:00

N.A.

Kawamoto

N.A.

N.A.

N.A.

12:00 – 13:00

Lunch

Lunch

Lunch

Lunch

Lunch

13:00 – 14:00

N.A.

Liang

Matsunuma

Explore A-Math

Tanaka

14:05 – 15:05

N.A.

Moriya

Noda

N.A.

Kawamoto

15:10 – 16:10

CREST (stability)

Tangiku

Matsui

N.A.

Kamakura

16:15 – 17:15

CREST (SCA)

N.A.

N.A.

F.M.

N.A.

17:30 – 19:00

CREST (math all)

N.A.

N.A.

F.M.

N.A.

                                      (Lectures; Seminars; Faculty Meetings; Not Available )

 

1.      Group Seminar on Mathematics (1st semester @ Zoom).

·     B3 Seminar (Matsui) on Theory of Probability and Random Processes.

·     B3 Seminar (Noda) on Mathematics in Phase Transitions and Critical Behavior.

·     B4 Seminar (Matsunuma) on Sandpile models.

·     B4 Seminar (Tangiku) on Stochastic Differential Equations.

·     M1 Seminar (Liang) on the contact process with dynamic edges on Z.

·     M1 Seminar (Moriya) on Random Graph Dynamics.

·     M1 Seminar (Tanaka) on Stochastic Calculus for Finance.

·     M2 Seminar (Kamakura) on Markov Chains and Mixing Times.

·     M2 Seminar (Kawamoto) on Non-intersection probability of random walks; Self-avoiding walk in 4 dimensions.

·     D4 Seminar (Kamijima) on Oriented percolation on the BCC lattice.

·     CREST Seminar (Fukushima-Kimura, Toyokawa) on Stability of energy landscape.

·     CREST Seminar (Fukushima-Kimura, Kamijima, Kamakura) on Stochastic cellular automata (SCA).

·     CREST Seminar (Fukushima-Kimura, Aoki, Kamijima, Toyokawa, Ishibashi, Kamakura).

 

2.      The World of Science and Technology（科学・技術の世界：数学のたのしみ） (1st semester, Tuesdays 8:45–10:15 @ ELMS); WeBWorK.

 

3.      Explore Advanced Mathematics（数学独立探求I） (1st semester, Thursdays 13:00–14:30 @ Zoom).

 

4.      Explore Basic Mathematics（数学基礎探求） (1st semester, Fridays 8:45–10:15 @ Zoom).

 

5.      Calculus II（微分積分学II） (2nd semester, Tuesdays & Wednesdays 13:00–14:30 @ Multimedia Education Bldg ?-???); WeBWorK for self-studies (need ELMS ID & Password).

 

6.      Introduction to Statistics（確率・統計入門） (2nd semester, Wednesdays 8:45–10:15 @ Science Bldg 3-309).

 

7.      Analytic Studies: Phase Transition and Critical Behavior of Oriented Percolation（数理解析学講義：有向パーコレーションの相転移・臨界現象） (2nd semester, Mondays 10:30–12:00 @ Science Bldg 3-204).

 

 

                        VI.          Curriculum vitae

 

·     August 2020 – present

Associate editor of Taiwanese Journal of Mathematics.

 

·     March 2020 – present

Associate editor of Mathematical Physics, Analysis and Geometry.

 

·     February 2020 – present

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

 

·     September 2015 – August 2019

Councilor of the Bernoulli Society.

 

·     Excellent Teachers 2018, 2015, 2012, 2011

The Hokkaido University President’s Award for Teaching Excellence in 2013 and in 2012.

 

·     April 2011 – January 2020

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

 

·     March 2008 – March 2011

Tenure-track assistant professor of Creative Research Institution SOUSEI, 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 “Analyses of the Critical Behavior for the Contact Process based on a Percolation Structure” supervised by Professor Takashi Hara.

 

·     April 1994 – March 1996

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

Awarded M.Sc. for the thesis “Approach to Fractal Growth Phenomena” supervised by Professor Takashi Hara.

 

·     April 1990 – March 1994

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

Awarded B.Sc. for the thesis “Recurrent in the Plane, Transient in Space” supervised by Professor Kohei Uchiyama.