Akira
Sakai
Associate professor
Hokkaido University
North 10, West 8, Kita-ku, Sapporo
Hokkaido 060-0810, JAPAN
Email: sakai
at math.sci.hokudai.ac.jp
Contents
Updated: April 12, 2012.
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, and associated scaling limits. For example, the Ising model exhibits a magnetic phase transition; it takes
on positive spontaneous magnetization when the temperature of the system is
turned down below its critical value. 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, self-avoiding walk, percolation, the contact process (a model for the spread of an infection) and random walk with reinforcement.
1.
L.-C. Chen and A. Sakai.
Asymptotic behavior of critical two-point functions for long-range
statistical-mechanical models in high dimensions.
2.
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.
3.
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.
4.
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.
5.
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.
6.
A. Sakai.
Applications of
the lace expansion to statistical-mechanical models.
A chapter in Analysis and
Stochastics of Growth Processes and Interface Models (Oxford University
Press, 2008).
7.
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.
8.
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.
9.
A. Sakai.
Diagrammatic bounds on the
lace-expansion coefficients for oriented percolation.
10. M. Holmes and A.
Sakai.
Senile reinforced random
walks.
Stochastic Process. Appl. 117 (2007): 1519–1539.
11. A. Sakai.
Lace expansion for the Ising
model.
Comm.
Math. Phys. 272 (2007): 283–344. arXiv:math-ph/0510093.
12. 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.
13. A. Sakai.
Mean-field behavior
for the survival probability and the percolation point-to-surface connectivity.
J.
Stat. Phys. 117 (2004): 111–130.
14. 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.
15. 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.
16. A. Sakai.
Hyperscaling inequalities for the
contact process and oriented percolation.
J.
Stat. Phys. 106 (2002): 201–211.
17. A. Sakai.
Mean-field critical behavior
for the contact process.
J.
Stat. Phys. 104 (2001): 111–143.
1.
Asymptotic
behavior of the critical two-point functions for
statistical-mechanical models with power-law decaying potentials.
·
VU
Probability Seminar (March 19, 2012) at Vrije Universiteit Amsterdam. The Netherlands.
·
New
Zealand Probability Workshop & Australia and New Zealand Applied
Probability Workshop (January 23–27,
2012) at the University of Auckland. New Zealand.
2.
Asymptotic
behavior in Zd of the critical two-point functions for
long-range statistical-mechanical models in high dimensions.
·
The 7th
HU and SNU Symposium on Mathematics “Recent Developments in Mathematical
Analysis and Related Fields” (November 16–17, 2011) at Seoul National University. South Korea.
3.
Rigorous
analyses for critical phenomena.
·
The seminar
for active researchers “Let’s
Enjoy Mathematical Sciences” (September 5–6, 2011) at Hokkaido University. Japan.
4.
Mathematics
for critical phenomena.
·
The Kinosaki Seminar (February 14–18, 2011) at Kinosaki Community Center. Japan.
5.
Application
of the lace expansion to the φ4
model.
·
The
NYUADI workshop “Probability
Theory, Statistical Physics and Applications” (January 16–20, 2011) at NYU Abu Dhabi
Institute. UAE.
1.
The
RIMS workshop “Applications of
Renormalization Group Methods in Mathematical Sciences” (September 12–14, 2011) at Kyoto University,
Japan.
2.
The
SPA Satellite workshop “Universality
and Scaling Limits in Probability and Statistical Mechanics” (August
30–September 3, 2010) at
Hokkaido University, Japan.
V.
Teaching (April 2012 – February
2013)
1.
Linear Algebra I (Semester
1, Friday 13:00–14:30 @ Center for RDHE.,
Room E311)
2.
Basic Mathematical Science (Semester 1, Friday 10:30–12:00 @ Science #3,
Room 309)
3.
Seminar on Mathematics (Semesters
1)
·
B4
Seminar on Branching Processes (Monday 9:00–12:00 @ Science #4, Room 401)
·
M1
Seminar on Infinite Particle Systems (Monday 14:00–17:00 @ Science #3,
Room 204)
·
M2
Seminar on Random Pinning Models (Tuesday 10:30–12:30 @ Science #3, Room 513)
·
M2
Seminar on Random Walk Intersections (Tuesday 13:00–15:00 @ Science #3,
Room 513)
4.
Linear Algebra II (Semester
2, Tuesday 13:00–14:30)
5.
Analysis F (Semester 2,
Friday 8:45–10:15)
6.
Seminar on Mathematics (Semesters
2)
·
April 2011 – present
Associate professor of the Department of Mathematics at
Hokkaido University.
Japan.
·
March 2008 – March 2011
Tenure-track assistant professor of Creative Research Institution SOUSEI
at Hokkaido University.
Japan.
·
April 2006 – February 2008
Lecturer in Probability of the Department of Mathematical Sciences
at the University of Bath.
UK.
·
April 2004 – March 2006
Postdoctoral researcher of Wiskunde en Informatica at Technische Universiteit Eindhoven
(TU/e). The Netherlands.
·
January 2003 – March 2004
Postdoctoral researcher of the Interacting-Stochastic-Systems
(ISS) group at EURANDOM. The Netherlands.
·
January 2001 – December 2002
Postdoctoral researcher of the Department of Mathematics at the University
of British Columbia.
Canada.
·
April 1996 – December 2000
Ph.D. study in Applied Physics at 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 at 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 at
Tokyo Institute of Technology. Japan.
Awarded B.Sc. for the thesis “Recurrent in
the Plane, Transient in Space” supervised by Professor Kohei Uchiyama.