Akira
Sakai （坂井 哲）
Associate professor
Hokkaido University
Nishi 8-chome, Kita 10-jo, Kita-ku, Sapporo
Hokkaido 060-0810, JAPAN
Email: sakai at math.sci.hokudai.ac.jp
Contents
Updated: May 5, 2017.
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,
· the φ^{4} 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),
· random walk with reinforcement.
1. S. Handa, M.
Heydenreich and A. Sakai. Mean-field
bound on the 1-arm exponent for Ising ferromagnets in high dimensions. Preprint (2016). arXiv:1612.08809.
2. 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. To appear in Plant & Cell
Physiology (2017).
3. 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.
4. A. Sakai. Application of the lace expansion to the
φ^{4} model. Commun. Math.
Phys. 336 (2015): 619–648.
The published
version incorporates a few corrections to arXiv:1403.5714.
5. L.-C. Chen and
A. Sakai. Critical two-point
functions for long-range statistical-mechanical models in high dimensions. Ann. Prob. 43 (2015): 639–681.
arXiv:1204.1180.
6. L.-C. Chen and
A. Sakai. Asymptotic behavior of
the gyration radius for long-range self-avoiding walk and long-range oriented
percolation. Ann. Prob. 39
(2011): 507–548. arXiv:1002.0875.
7. 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.
8.
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.
9. L.-C. Chen and
A. Sakai. Critical behavior and the
limit distribution for long-range oriented percolation. II: Spatial
correlation. Probab.
Theory Related Fields 145 (2009): 435–458. arXiv:0804.2039.
10. 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).
11. 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.
12. L.-C. Chen and
A. Sakai. Critical behavior and the
limit distribution for long-range oriented percolation. I. Probab.
Theory Related Fields
142 (2008): 151–188. arXiv:0703455.
13. A. Sakai. Diagrammatic bounds on the
lace-expansion coefficients for oriented percolation. arXiv:0708.2897.
14. M. Holmes and A.
Sakai. Senile reinforced random
walks. Stochastic
Process. Appl. 117 (2007): 1519–1539.
15. A. Sakai. Lace expansion for the Ising model. Commun.
Math. Phys. 272
(2007): 283–344. arXiv:math-ph/0510093.
16.
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 Related Fields 132 (2005): 438–470. arXiv:math/0402050.
17.
A.
Sakai. Mean-field behavior for the
survival probability and the percolation point-to-surface connectivity. J.
Stat. Phys. 117 (2004): 111–130.
18.
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):
710–769. arXiv:math/0402049.
19.
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.
20.
A.
Sakai. Hyperscaling
inequalities for the contact process and oriented percolation. J.
Stat. Phys. 106 (2002): 201–211.
21.
A.
Sakai. Mean-field critical behavior
for the contact process. J.
Stat. Phys. 104 (2001): 111–143.
Year 2017
1. T.B.A.
·
MSJ
Fall Meeting (September 11–14). Yamagata University, Japan.
2. Critical behavior for oriented percolation:
From a mathematically rigorous standpoint.
·
Summer School in Mathematical
Physics (August 25–27). The University of Tokyo, Japan.
3. The lace expansion for percolation on the
BCC lattice in d ≥ 9 dimensions.
·
Seminar on Probability (July 18). Osaka University, Japan.
4. Mean-field bound on the 1-arm exponent for
high-dimensional Ising ferromagnets.
·
Physical and
Mathematical Approaches to Interacting Particle Systems – In Honer of
70^{th} Birthday of Herbert Spohn (January 11–12). Tokyo
Institute of Technology, Japan.
Year 2016
1.
Mean-field
bound on the 1-arm exponent for Ising ferromagnets in high dimensions.
·
3^{rd}
Workshop on Probability Theory and its Applications (December 13–16).
Korea Institute for Advanced Study, South Korea.
·
2016 TMS Annual
Meeting (December 11–12). National Dong Hwa University, Taiwan.
·
15^{th}
Stochastic Analysis on Large Scale Interacting Systems (November 2–4).
The University of Tokyo, Japan.
· International
Conference on Probability Theory and Statistical Physics (March 25–27). NYU
Shanghai, China.
· 2016
Spring Probability Workshop (March 7–9). Academia Sinica, Taiwan.
2.
The
lace expansion for the nearest-neighbor models on the BCC lattice.
·
MSJ
Fall Meeting (September 15–18). Kansai University, Japan.
· The BIRS Workshop
“Random
Structures in High Dimensions” (June 26–July 1). Casa Matemática
Oaxaca, Mexico.
3.
Rigorous
analysis of critical behavior for statistical-mechanical models of polymers.
·
Hokkaido
Young Polymer Scientists Workshop (September 2–3). Jozankei View Hotel, Japan.
4.
Random
walk and its dimensional dependence.
· Science
Globe for New Students (June 15). Hokkaido University, Japan.
5.
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.
1. The 1-day workshop “Recent Progress
in Probability Theory and Its Applications” (July 28, 2017). Hokkaido
University, Japan.
2. 2017
Spring Probability Workshop (March 6–8, 2017). Academia Sinica, Taiwan.
3. The 2^{nd}
workshop on Universality and Scaling Limits in Probability and Statistical
Mechanics (August 5–9,
2013). Hokkaido University, Japan.
4. International
Workshop on Potential Theory (February 4, 2013). Hokkaido University,
Japan.
5. The RIMS workshop “Applications of
Renormalization Group Methods in Mathematical Sciences” (September 12–14, 2011). Kyoto University,
Japan.
6. The SPA Satellite workshop “Universality
and Scaling Limits in Probability and Statistical Mechanics” (August
30–September 3, 2010).
Hokkaido University, Japan.
V.
Teaching (April 2017 – February
2018)
1^{st} Semester |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
8:45 – 10:15 |
L.A. (P) |
N.A. |
N.A. |
N.A. |
B.M.S. (P) |
10:30 – 12:00 |
L.A. (L) |
N.A. |
Handa |
Kamijima |
B.M.S. (L) |
12:00 – 13:00 |
Lunch |
Lunch |
Lunch |
Lunch |
Lunch |
13:00 – 14:30 |
L.A. (M) |
N.A. |
Kamijima |
Anyone |
Calculus (P) |
14:45 – 16:15 |
N.A. |
N.A. |
Kamakura |
Mitobe |
Calculus (L) |
16:30 – 18:00 |
N.A. |
N.A. |
Natori |
Mizushiri |
O.H. |
(Lectures-Preparation-Marking; Office Hour; Seminars; Not Available )
1. Linear
Algebra I (1^{st} Semester, Mondays 10:30–12:00 @ Multimedia Education Bldg E-301).
2. Basic
Mathematical Science (1^{st} Semester, Fridays 10:30–12:00 @ Science
Bldg 5-301).
3. Calculus
I (1^{st} Semester, Fridays 14:45–16:15 @ Multimedia Education Bldg E-311).
4. Freshman Seminar
(2^{nd} Semester, Thursdays 16:30–18:00 @ Multimedia Education Bldg).
5. Calculus II (2^{nd}
Semester, Fridays 14:45–16:15 @ Multimedia Education Bldg).
6. Statistics (2^{nd}
Semester, @ Science Bldg).
7. Seminar on
Mathematics (Wednesdays and Thursdays @ Science Bldg 4-506).
·
B3 Seminar (Kamakura)
on Random Walk and Stochastic Calculus.
·
B4 Seminar (Mizushiri)
on Percolation.
·
B4 Seminar (Natori) on
From Basic Probability to Statistics.
·
M2 Seminar (Mitobe) on
Probability with Martingales.
·
D1 Seminar (Kamijima)
on The Lace Expansion on the
Body-centered Cubic Lattice.
·
D2 Seminar (Handa) on
The Ising 1-spin expectation at and below
the critical temperature.
· September
2015 – August 2019
Councilor of the Bernoulli Society.
· March
2016
Selected as one
of Excellent
Teachers 2015.
· March
2014
The Hokkaido University President’s
Award for Teaching Excellence 2013.
· March
2013
The Hokkaido University President’s
Award for Teaching
Excellence 2012.
· March
2012
Selected as one
of Excellent
Teachers 2011.
· 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.