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

 

Contents

I. Fields of interest

II. Research papers

III. Recent public talks

IV. Workshops

V. Teaching

VI. Curriculum vitae

 

Updated: April 29, 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.

J. Stat. Phys. 163 (2016): 754–764. 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.

arXiv:0708.2897.

 

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

 

Year 2016

 

1.       TBA.

·     Workshop on Probability and its Applications (December 13–16). Korea Institute for Advanced Study, South Korea.

 

2.       The lace expansion for the nearest-neighbor models on the BCC lattice.

·     The BIRS Workshop “Random Structures in High Dimensions” (June 26–July 1). Casa Matemática Oaxaca, Mexico.

 

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

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

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

 

4.       Self-avoiding walk on random conductors.

·     The IMI Workshop “Mathematical Quantum Field Theory and Related Topics” (June 6–8). Kyushu University, Japan.

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

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

 

Year 2015

 

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

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

 

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

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

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

 

3.       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). The Institut Henri Poincaré, France.

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

 

Previous years

 

 

                         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 (April 2016 – July 2016)

 

2nd Semester

Monday

Tuesday

Wednesday

Thursday

Friday

  8:45 – 10:15

Calculus (P)

NA

NA

NA

NA

10:30 – 12:00

Calculus (L)

Handa

NA

Handa & Kamijima

Chino

12:00 – 13:00

Lunch

Lunch

Lunch

Lunch

Lunch

13:00 – 14:30

Calculus (M)

NA

NA

NA

Mitobe

14:45 – 16:15

Calculus (M)

NA

NA

Kamijima

Seki

16:30 – 18:00

OH

NA

NA

Natori

Seno

18:15 – 19:45

OH

NA

NA

NA

NA

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

 

1.      Calculus I (Mondays 10:3012:00 @ Multimedia Education Bldg N281).

 

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

·     B4 Seminar (Natori) on Percolation.

·     M1 Seminar (Mitobe) on Introduction to Stochastic Integration.

·     M2 Seminar (Seki) on The Spread of Infections on Evolving Scale-free Networks.

·     M2 Seminar (Seno) on The Spread of Infections on Evolving Scale-free Networks.

·     M2 Seminar (Kamijima) on the Lace Expansion for Self-avoiding Walk on the BCC Lattice.

·     D1 Seminar (Handa) on the Mean-field Bound on the Ising 1-arm Exponent.

·     D3 Seminar (Chino) on the Pinning Model in a Stable Environment.

 

 

                         VI.          Curriculum vitae

 

·     September 2015 – August 2019

Councilor of the Bernoulli Society.

·     March 2014

The Hokkaido President’s Award for Teaching Excellence 2013.

·     March 2013

The Hokkaido President’s Award for Teaching Excellence 2012.

·     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.