Akira Sakai

Associate professor

Department of Mathematics

Hokkaido University

Nishi 8-chome, Kita 10-jo, Kita-ku, Sapporo

Hokkaido 060-0810, JAPAN

Email: sakai at math.sci.hokudai.ac.jp



I. Fields of interest

II. Research papers

III. Recent public talks

IV. Workshops

V. Teaching

VI. Curriculum vitae


Updated: February 4, 2016.



                           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 exhibit the following phase transition: it takes 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, the φ4 model (in lattice scalar-field theory), self-avoiding walk (a model for linear polymers), percolation (for random media), the contact process (for the spread of an infectious disease) and random walk with reinforcement.



                        II.          Research papers


1.           Y. Chino and A. Sakai.

The quenched critical point for self-avoiding walk on random conductors.

To appear in J. Stat. Phys. arXiv:1508.01262.


2.           A. Sakai.

Application of the lace expansion to the φ4 model.

Comm. Math. Phys. 336 (2015): 619–648. The published version incorporates a few corrections to arXiv:1403.5714.


3.           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.


4.           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.


5.           A. Sakai.

Large-time asymptotics of the gyration radius for long-range statistical-mechanical models.

RIMS Kokyuroku Bessatsu B21 (2011): 53–62. arXiv:0912.5117.


6.           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): 801–894. arXiv:0809.1712.


7.           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): 435458. arXiv:0804.2039.


8.           A. 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).


9.           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): 10011049. arXiv:0712.0312.


10.      L.-C. Chen and A. Sakai.

Critical behavior and the limit distribution for long-range oriented percolation. I.

Probab. Theory Relat. Fields 142 (2008): 151188. arXiv:0703455.


11.      A. Sakai.

Diagrammatic bounds on the lace-expansion coefficients for oriented percolation.



12.      M. Holmes and A. Sakai.

Senile reinforced random walks.

Stochastic Process. Appl. 117 (2007): 15191539.


13.      A. Sakai.

Lace expansion for the Ising model.

Comm. Math. Phys. 272 (2007): 283344. arXiv:math-ph/0510093.


14.      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): 438470. arXiv:math/0402050.


15.      A. Sakai.

Mean-field behavior for the survival probability and the percolation point-to-surface connectivity.

J. Stat. Phys. 117 (2004): 111130.


16.      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): 710769. arXiv:math/0402049.


17.      M. Holmes, A.A. Járai, A. Sakai and G. Slade.

High-dimensional graphical networks of self-avoiding walks.

Canad. J. Math. 56 (2004): 77114.


18.      A. Sakai.

Hyperscaling inequalities for the contact process and oriented percolation.

J. Stat. Phys. 106 (2002): 201211.


19.      A. Sakai.

Mean-field critical behavior for the contact process.

J. Stat. Phys. 104 (2001): 111143.



                    III.          Recent public talks


1.           Mean-field bound on the 1-arm exponent for Ising ferromagnets in high dimensions.

·          Conference on Probability Theory and Statistical Physics (March 25-27, 2016). NYU Shanghai, China.


2.           Mean-field behavior for the nearest-neighbor models on the BCC lattice.

·          Probability Seminar (March 11, 2016). National Central University, Taiwan.


3.           Self-avoiding walk on random conductors.

·          2016 Spring Probability Workshop (March 7–9, 2016). Academia Sinica, Taiwan.

·          NZ Probability Workshop 2016 (January 3–9, 2016). Scenic Hotel Bay of Islands, New Zealand.


4.           Critical points for self-avoiding walk on random conductors.

·          Summer School on Dirichlet Form and Stochastic Analysis (August 24–28, 2015). Kansai University, Japan.


5.           Critical two-point function for the φ4 model in high dimensions.

·          IMS Workshop on Stochastic Processes in Random Media (May 4–15, 2015). The Institute for Mathematical Sciences, Singapore.

·          Kyushu Probability Seminar (April 24, 2015). Kyushu University, Japan.


6.           Critical correlation in high dimensions for long-range models with power-law couplings.

·          The IHP Workshop “Spin Glasses, Random Graphs and Percolation” (February 16–20, 2015). The Institut Henri Poincaré, France.

·          Niigata Probability Workshop (January 2223, 2015). Niigata University, Japan.


7.           General idea and recent results on the lace expansion.

·          The International Mathematical Meeting and the Annual Meeting of the TMS (December 6–7, 2014). National Cheng Kung University, Taiwan.


8.           Critical two-point function for the lattice φ4 model in dimensions d > 4.

·          UBC Probability Seminar (September 10, 2014). The University of British Columbia, Canada.

·          Sapporo Mathematical Physics Workshop (September 1–2, 2014). Hokkaido University, Japan.


9.           An attempt to prove mean-field behavior for percolation in 7 dimensions.

·          NZ Probability Workshop (January 6–10, 2014). The Distinction Te Anau Hotel, New Zealand.

·          Niigata Probability Workshop (December 5–6, 2013). Niigata University, Japan.


10.      The lace expansion: rigorous analysis for critical phenomena.

·          The Japanese Society for Mathematical Biology Fall Meeting (September 11–13, 2013). Shizuoka University, Japan.


11.      Recent progress in the lace expansion.

·          New Directions in Probability (May 30–June 4, 2013). ISI Bangalore, India.


12.      Application of the lace expansion to the φ4 model.

·          2013 NCTS Workshop on Stochastic Processes and Related Topics (March 14–15, 2013), National Tsing Hua University, Taiwan.

·          The Annual Probability Symposium (December 18–21, 2012). Kyoto University, Japan.

·          The MFO Workshop “Scaling Limits in Models of Statistical Mechanics” (September 915, 2012). The Mathematisches Forschungsinstitut Oberwolfach, Germany.

·          The Modena Workshop “Disorder in Probability and Statistical Mechanics” (June 25–29, 2012). Università di Modena e Reggio Emilia, Italy.


Previous public talks



                    IV.          Workshops


1.           The 2nd workshop on Universality and Scaling Limits in Probability and Statistical Mechanics (August 59, 2013), Hokkaido University, Japan.


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


3.           The RIMS workshop “Applications of Renormalization Group Methods in Mathematical Sciences” (September 1214, 2011), Kyoto University, Japan.


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



                       V.          Teaching (October 2015 – February 2016)


2nd Semester






  8:45 – 10:15






10:30 – 12:00






12:00 – 13:00






13:00 – 14:30






14:45 – 16:15






16:30 – 18:00






18:15 – 19:45






                                                      (Lectures-Preparation-Marking; Office Hour; Seminars; Not Available)


1.           Linear Algebra II (Mondays 13:0014:30 @ Multimedia Education Bldg E214).


2.           Seminar on Mathematics (Wednesdays @ Science Bldg 4-411, Thursdays and Fridays @ Science Bldg 4-408).

·          B4 Seminar (Chu) on Martingale, Random Walks and Electric Networks.

·          B4 Seminar (Mitobe) on Classical and Spatial Stochastic Processes.

·          B4 Seminar (Natori) on Percolation.

·          M1 Seminar (Seki) on Random Walks and Voter Models.

·          M1 Seminar on (Seno) Epidemic Models in Random Environments.

·          M1 Seminar (Kamijima) on Hydrodynamic Limit for Lattice Gas Models.

·          M1 Seminar (Laine) on Transfer-matrix Approach for Self-avoiding Walk.

·          M2 Seminar (Abe) on Dissipation and High Disorder.

·          M2 Seminar (Kawahara) on Brownian Motion, Obstacles and Random Media.

·          M2 Seminar (Handa) on Critical Behavior for Percolation and  the Ising Model.

·          D3 Seminar (Chino) on Self-avoiding Walk on Random Conductors.



                    VI.          Curriculum vitae


·          September 2015 – August 2019

Councilor of the Bernoulli Society.


·          April 2011 – present

Associate professor of the Department of Mathematics, 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.