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: April 29, 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 exhibit the following phase transition: it takes 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) and random walk with reinforcement.
1.
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.
2.
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.
3.
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.
4.
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.
5.
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.
6.
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.
7.
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.
8.
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).
9.
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.
10.
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.
11.
A. Sakai.
Diagrammatic bounds on the
lace-expansion coefficients for oriented percolation.
12.
M. Holmes and A. Sakai.
Senile reinforced random walks.
Stochastic Process. Appl. 117 (2007): 1519–1539.
13.
A.
Sakai.
Lace expansion for the Ising
model.
Comm.
Math. Phys. 272 (2007): 283–344. arXiv:math-ph/0510093.
14.
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.
15.
A.
Sakai.
Mean-field behavior
for the survival probability and the percolation point-to-surface connectivity.
J.
Stat. Phys. 117 (2004): 111–130.
16.
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.
17.
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.
18.
A.
Sakai.
Hyperscaling inequalities for the
contact process and oriented percolation.
J.
Stat. Phys. 106 (2002): 201–211.
19.
A.
Sakai.
Mean-field critical behavior
for the contact process.
J.
Stat. Phys. 104 (2001): 111–143.
Year 2016
1. TBA.
·
Workshop on Probability and its Applications (December
13–16). Korea Institute for Advanced Study, South Korea.
2. The lace expansion for the nearest-neighbor models on the BCC lattice.
·
The BIRS Workshop “Random Structures
in High Dimensions” (June 26–July 1). Casa Matemática
Oaxaca, Mexico.
3. Mean-field bound on the 1-arm exponent for Ising ferromagnets in high
dimensions.
·
International Conference
on Probability Theory and Statistical Physics (March 25–27). NYU
Shanghai, China.
·
2016
Spring Probability Workshop (March 7–9). Academia Sinica,
Taiwan.
4. 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.
Year 2015
1. Critical points for self-avoiding walk on
random conductors.
·
Summer
School on Dirichlet Form and Stochastic Analysis (August 24–28). Kansai
University, Japan.
2. Critical two-point function for the φ^{4} model in high dimensions.
·
IMS Workshop on
Stochastic Processes in Random Media (May 4–15). The Institute for
Mathematical Sciences, Singapore.
·
Kyushu Probability Seminar (April 24). Kyushu
University, Japan.
3. 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). The Institut
Henri Poincaré, France.
·
Niigata
Probability Workshop (January 22–23). Niigata University, 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 2016 – July 2016)
2^{nd} Semester |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
8:45 – 10:15 |
Calculus (P) |
NA |
NA |
NA |
NA |
10:30 – 12:00 |
Calculus (L) |
Handa |
NA |
Handa & Kamijima |
Chino |
12:00 – 13:00 |
Lunch |
Lunch |
Lunch |
Lunch |
Lunch |
13:00 – 14:30 |
Calculus (M) |
NA |
NA |
NA |
Mitobe |
14:45 – 16:15 |
Calculus (M) |
NA |
NA |
Kamijima |
Seki |
16:30 – 18:00 |
OH |
NA |
NA |
Natori |
Seno |
18:15 – 19:45 |
OH |
NA |
NA |
NA |
NA |
(Lectures-Preparation-Marking; Office Hour; Seminars; Not Available)
1.
Calculus I (Mondays 10:30–12:00 @ Multimedia Education Bldg N281).
2.
Seminar on Mathematics (Thursdays and
Fridays @ Science Bldg 4-408).
·
B4 Seminar (Natori) on
Percolation.
·
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.
·
D3 Seminar (Chino) on
the Pinning Model in a Stable Environment.
· September
2015 – August 2019
Councilor of the Bernoulli Society.
· March
2014
The Hokkaido President’s Award for
Teaching Excellence 2013.
· March
2013
The Hokkaido President’s Award for
Teaching Excellence 2012.
· 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.