Akira
Sakai
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 12, 2015.
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, the φ^{4} model (in 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.
1.
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.
2.
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.
3.
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.
4.
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.
5.
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.
6.
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.
7.
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).
8.
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.
9.
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.
10. A. Sakai.
Diagrammatic bounds on the
lace-expansion coefficients for oriented percolation.
11. M. Holmes and A.
Sakai.
Senile reinforced random
walks.
Stochastic Process. Appl. 117 (2007): 1519–1539.
12. A. Sakai.
Lace expansion for the Ising
model.
Comm.
Math. Phys. 272 (2007): 283–344. arXiv:math-ph/0510093.
13. 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.
14. A. Sakai.
Mean-field behavior
for the survival probability and the percolation point-to-surface connectivity.
J.
Stat. Phys. 117 (2004): 111–130.
15. 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.
16. 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.
17. A. Sakai.
Hyperscaling inequalities for the
contact process and oriented percolation.
J.
Stat. Phys. 106 (2002): 201–211.
18. A. Sakai.
Mean-field critical behavior
for the contact process.
J.
Stat. Phys. 104 (2001): 111–143.
1.
Critical
two-point function for the φ^{4}
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.
2.
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 22–23,
2015). Niigata University, Japan.
3.
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.
4.
Critical
two-point function for the lattice φ^{4}
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.
5.
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.
6.
The
lace expansion: rigorous analysis for critical phenomena.
·
The Japanese Society
for Mathematical Biology Fall Meeting (September 11–13, 2013). Shizuoka University, Japan.
7.
Recent
progress in the lace expansion.
·
New Directions in Probability
(May 30–June 4, 2013). ISI
Bangalore, India.
8.
Application
of the lace expansion to the φ^{4}
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 9–15, 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.
9.
Asymptotic
behavior of the critical two-point functions for
statistical-mechanical models with power-law decaying potentials.
·
VU
Probability Seminar (March 19, 2012). Vrije Universiteit Amsterdam, the Netherlands.
·
New
Zealand Probability Workshop & Australia and New Zealand Applied
Probability Workshop (January 23–27,
2012). The University of Auckland, New Zealand.
10.
Asymptotic
behavior in Z^{d} of the critical two-point functions for
long-range statistical-mechanical models in high dimensions.
·
The 7^{th}
HU and SNU Symposium on Mathematics “Recent Developments in Mathematical
Analysis and Related Fields” (November 16–17, 2011). Seoul National University, South Korea.
11.
Rigorous
analyses for critical phenomena.
·
The Seminar
for Active Researchers “Let’s
Enjoy Mathematical Sciences” (September 5–6, 2011). Hokkaido University, Japan.
12.
Mathematical
analysis for critical phenomena.
·
The Kinosaki Seminar (February 14–18, 2011). Kinosaki Community Center, Japan.
1.
The 2^{nd}
workshop on Universality and Scaling Limits in Probability and Statistical
Mechanics (August 5–9,
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 12–14, 2011), Kyoto University,
Japan.
4.
The
SPA Satellite workshop “Universality
and Scaling Limits in Probability and Statistical Mechanics” (August
30–September 3, 2010),
Hokkaido University, Japan.
V.
Teaching (April 2015 – August
2015)
1^{st} Semester |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
8:45 – 10:15 |
NA |
NA |
NA |
NA |
BMSU(P) |
10:30 – 12:00 |
NA |
Chino |
LA(P) |
Handa |
BMSU(L) |
12:00 – 13:00 |
Lunch |
Lunch |
Lunch |
Lunch |
Lunch |
13:00 – 14:30 |
LA(P) |
Kawahara |
LA(L) |
Chu |
Mitobe |
14:45 – 16:15 |
LA(L) |
Abe |
LA(M) |
Handa |
Seki |
16:30 – 18:00 |
LA(M) |
Seno |
LA(M) |
Kamijima |
Natori |
18:15 – 19:45 |
OH |
NA |
NA |
NA |
NA |
(Lectures-Preparation-Marking; Office Hour; Seminars; Not Available)
1.
Linear Algebra I (Semester 1, Monday 14:45–16:15 @
Multimedia Education Bldg E308; Wednesday 13:00–14:30 @ Multimedia Education Bldg N283).
2.
Basic Mathematical Science
for Undergrads (Semester 1, Friday
10:30–12:00 @ Science Bldg 5-201).
3.
Seminar on Mathematics (Semester
1 @ Science Bldg 4-408).
·
B4 (Chu) Seminar on Probability
Theory.
·
B4 (Mitobe)
Seminar on Classical and Spatial Stochastic Processes.
·
B4 (Natori) Seminar on Percolation.
·
M1 (Seki) Seminar on Random
Walks and Voter Models.
·
M1 (Seno) Seminar on Random
Graph Dynamics.
·
M1 (Kamijima)
Seminar on
???.
·
M2 (Abe) Seminar on Dissipation
and High Disorder.
·
M2 (Kawahara) Seminar on Brownian
Motion, Obstacles and Random Media.
·
M2 (Handa)
Seminar on Functional Integral Representation for
Weakly Self-avoiding Walk.
·
D3 (Chino) Seminar on Random
Media.
·
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.