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: March 18, 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 degradation during cold acclimation in arabidopsis cells.
Preprint (2016).
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. Comm. 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. Probab. 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. Probab. 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 Relat. 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 Relat. 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. Comm.
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 Relat. 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. 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. |
Seminar |
Seminar |
Calculus (P) |
14:45 – 16:15 |
N.A. |
N.A. |
Seminar |
Seminar |
Calculus (L) |
16:30 – 18:00 |
N.A. |
N.A. |
Seminar |
Seminar |
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).
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).
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).
·
B3 Seminar (Kamakura)
on Random Walk and Stochastic Calculus.
·
B4 Seminar (Mizushiri)
on Percolation.
·
B4 Seminar (Natori) on
T.B.A.
·
M2 Seminar (Mitobe) on
T.B.A.
·
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.