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: December 9, 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 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.
In preparation.
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.
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.
2017
Spring Probability Workshop (March 6–8). Academia Sinica, Taiwan.
2.
The 2^{nd}
workshop on Universality and Scaling Limits in Probability and Statistical
Mechanics (August 5–9,
2013). Hokkaido University, Japan.
3.
International
Workshop on Potential Theory (February 4, 2013). Hokkaido University,
Japan.
4.
The
RIMS workshop “Applications of
Renormalization Group Methods in Mathematical Sciences” (September 12–14, 2011). Kyoto University,
Japan.
5.
The
SPA Satellite workshop “Universality
and Scaling Limits in Probability and Statistical Mechanics” (August
30–September 3, 2010).
Hokkaido University, Japan.
V.
Teaching (October 2016 – February
2017)
2^{nd} Semester |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
8:45 – 10:15 |
N.A. |
Basic Math D (P) |
N.A. |
Basic Math D (P) |
Analysis F (L) |
10:30 – 12:00 |
Natori |
Basic Math D (L) |
Handa |
Basic Math D (L) |
Kamijima |
12:00 – 13:00 |
Lunch |
Lunch |
Lunch |
Lunch |
Lunch |
13:00 – 14:00 |
N.A. |
Natori |
Seno |
Natori |
Natori |
14:00 – 15:00 |
N.A. |
N.A. |
Seki |
Basic Math D (M) |
Mitobe |
15:00 – 16:00 |
Basic Math D (P) |
N.A. |
N.A. |
Analysis F (P) |
Negishi |
16:00 – 17:00 |
Kaiseki Seminar |
N.A. |
Natori |
Analysis F (P) |
N.A. |
17:00 – 18:00 |
Kaiseki Seminar |
O.H. |
Basic Math D (P) |
O.H. |
Analysis F (M) |
(Lectures-Preparation-Marking; Office Hour; Seminars; Not Available )
1.
Basic Mathematics D (2^{nd} Semester,
Tuesdays and Thursdays 10:30–12:00
@ Science Bldg 3-309).
2.
Analysis F (2^{nd} Semester, Fridays 8:45–10:15 @ Science
Bldg 3-309).
3.
Hokudai-Tohokudai
Summer School (September 5–8 @ Ootaki Seminar House).
4.
Calculus I (1^{st} Semester, Mondays 10:30–12:00 @ Multimedia
Education Bldg N281).
5.
Seminar on Mathematics (Wednesdays and
Fridays @ Science Bldg 4-509).
·
B4 Seminar (Natori)
on Probability and Statistics.
·
B4 Seminar (Negishi) on Probability
and Complex Systems.
·
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.
· September
2015 – August 2019
Councilor of the Bernoulli Society.
· March
2016
Selected as one
of Excellent
Teachers 2015.
· March
2014
The Hokkaido 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.