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
IV. Organizing scientific meetings
Updated: December 13, 2019.
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 (for magnets),
· the φ^{4} model (in lattice scalar-field theory),
· self-avoiding walk (for linear polymers),
· lattice trees (for branched polymers),
· percolation (for random media),
· the contact process (for the spread of an infectious disease),
· random walk with reinforcement.
1.
S. Handa, K. Kamakura, Y.
Kamijima and A. Sakai. Finding optimal solutions by stochastic
cellular automata. Submitted. arXiv:1906.06645.
2.
Akira Sakai.
Crossover phenomena in the critical behavior
for long-range models with power-law couplings. To appear in RIMS Kokyuroku
Bessatsu.
arXiv:1812.10275.
3.
S. Handa, Y. Kamijima and A. Sakai.
A survey on the lace expansion for the nearest-neighbor
models on the BCC lattice. To
appear in Taiwanese
Journal of Mathematics. arXiv:1712.05573.
4.
L.-C. Chen and A. Sakai. Critical two-point function for
long-range models with power-law couplings: The marginal case for d ³ d_{c}. Commun.
Math. Phys. 372 (2019): 543–572 (the full-text view-only version). arXiv:1808.06789.
5.
S. Handa, M. Heydenreich and A. Sakai. Mean-field bound on the 1-arm
exponent for Ising ferromagnets in high dimensions. A chapter in Sojourns in Probability and
Statistical Physics - I (V. Sidoravicius ed.,
Springer, 2019). arXiv:1612.08809.
6.
A. Sakai and G. Slade. Spatial moments for high-dimensional
critical contact process, oriented percolation and lattice trees. Electron. J. Probab. 24 (2019): no. 65, 1–18. arXiv:1810.04011.
7.
Akira Sakai.
Hyperscaling for oriented percolation in 1+1
space-time dimensions. J. Stat. Phys. 171 (2018): 462–469
(the full-text view-only version). arXiv:1709.08291.
8.
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 decay during cold acclimation in arabidopsis
cells. Plant
Cell Physiol. 58 (2017): 1090–1102.
9.
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.
10.
Akira Sakai.
Application of the lace expansion to the φ^{4} model. Commun. Math.
Phys. 336 (2015): 619–648. arXiv:1403.5714.
11.
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.
12.
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.
13.
Akira Sakai.
Large-time asymptotics of the gyration radius
for long-range statistical-mechanical models. RIMS
Kokyuroku Bessatsu B21 (2011): 53–62. arXiv:0912.5117.
14.
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): no. 27, 801–894. arXiv:0809.1712.
15.
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.
16.
Akira 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).
17.
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.
18.
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.
19.
Akira Sakai.
Diagrammatic bounds on the lace-expansion coefficients for oriented
percolation. arXiv:0708.2897.
20.
M. Holmes and A. Sakai. Senile reinforced random walks. Stoch.
Proc. Appl. 117 (2007): 1519–1539.
21.
Akira Sakai. Lace expansion for the Ising model.
Commun.
Math. Phys. 272
(2007): 283–344. arXiv:math-ph/0510093.
22.
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.
23.
Akira Sakai. Mean-field behavior
for the survival probability and the percolation point-to-surface connectivity.
J.
Stat. Phys. 117 (2004): 111–130.
24.
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): no. 24, 710–769. arXiv:math/0402049.
25.
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.
26.
Akira Sakai. Hyperscaling
inequalities for the contact process and oriented percolation. J. Stat. Phys.
106 (2002): 201–211.
27.
Akira Sakai. Mean-field critical behavior
for the contact process. J. Stat. Phys.
104 (2001): 111–143.
Year 2019
1. Finding optimal solutions by stochastic
cellular automata.
·
7^{th}
Wellington Workshop in Probability and Mathematical Statistics (December 5–7).
Wellington, New Zealand.
·
Workshop
on Probabilistic Methods in Statistical Mechanics of Random Media and Random
Fields (May 27–31). Universiteit Leiden, the Netherlands.
·
AIMaP 1-day Workshop
(March 26). RIES, Hokkaido University, Japan.
2. Critical two-point function for long-range
models with power-law couplings: The marginal case for d ³ d_{c}.
·
The 12^{th}
MSJ-SI “Stochastic Analysis, Random Fields and Integrable Probability” (July
31–August 9). Kyushu University, Japan.
·
Seminar in
Statistics (January 16). The University of Auckland, New Zealand.
Year 2018
1.
Critical
two-point function for long-range models with power-law couplings: The marginal
case for d ³ d_{c}.
·
17^{th}
International Symposium “Stochastic Analysis on Large-scale Interacting Systems”
(November 5–8). RIMS, Kyoto
University, Japan.
·
High-dimensional Critical Phenomena in Random
Environments (September 24–26). The University of Bristol, UK.
·
2018
Spring Probability Workshop (June 4–8). Academia Sinica,
Taiwan.
2.
Hyperscaling for oriented percolation in 1+1 space-time dimensions.
·
Rikkyo Math Phys
Seminar (May 23). Rikkyo University, Japan
·
NUS Probability Seminar (February 12). National University of Singapore, Singapore.
Year 2017
1.
Hyperscaling for oriented percolation in 1+1 space-time dimensions.
·
NTU Math Colloquium (November 27).
National Taiwan University, Taiwan.
·
MSJ
Fall Meeting (September 11–14). Yamagata University, Japan.
3.
Critical
behavior for oriented percolation: From a
mathematically rigorous standpoint.
·
Summer School in Mathematical
Physics (August 25–27). The
University of Tokyo, Japan.
4.
The
lace expansion for self-avoiding walk and percolation on the BCC lattice.
·
Seminar on
Probability (July 18). Osaka
University, Japan.
5.
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.
IV.
Organizing scientific meetings
1.
The 10^{th} World Congress in Probability and
Statistics (August 17–21, 2020).
Seoul National University, South Korea.
2.
The
3^{rd} workshop on Universality and Scaling Limits in Probability and
Statistical Mechanics (July 13–17,
2020). Hokkaido University, Japan.
3.
The
RIMS Workshop “Rigorous
Statistical Mechanics and Related Topics” (November 18–21, 2019). RIMS, Kyoto University, Japan.
4.
The
1-day workshop “Recent
Progress in Probability Theory and Its Applications” (July 28, 2017).
Hokkaido University, Japan.
5.
2017
Spring Probability Workshop (March 6–8, 2017). Academia Sinica, Taiwan.
6.
The 2^{nd}
workshop on Universality and Scaling Limits in Probability and Statistical Mechanics
(August 5–9, 2013). Hokkaido
University, Japan.
7.
International
Workshop on Potential Theory (February 4, 2013). Hokkaido University,
Japan.
8.
The
RIMS workshop “Applications
of Renormalization Group Methods in Mathematical Sciences” (September 12–14, 2011). Kyoto University, Japan.
9.
The
SPA Satellite workshop “Universality
and Scaling Limits in Probability and Statistical Mechanics” (August 30–September 3, 2010). Hokkaido
University, Japan.
V.
Teaching (April 2019 – February 2020)
2^{nd} semester |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
8:45 – 10:15 |
N.A. |
Calculus I(L) |
N.A. |
N.A. |
Analysis F(L) |
10:30 – 12:00 |
N.A. |
Calculus I(P) |
N.A. |
N.A. |
Analysis F(P) |
12:00 – 13:00 |
Lunch |
Lunch |
Lunch |
Lunch |
Lunch |
13:00 – 14:30 |
CREST(Stability) |
N.A. |
Kamakura |
Nishimura |
Moriya |
14:45 – 16:15 |
CREST(SCA) |
Kawamoto |
Tanaka |
Mizushiri |
Matsunuma |
16:30 – 18:00 |
N.A. |
Kamijima |
Noda |
N.A. |
N.A. |
18:00 – 20:00 |
HITACHI |
Liang
& O.H. |
N.A. |
N.A. |
N.A. |
(Lectures-Preparation; Office Hour; Seminars; Not Available )
1. Seminar on
Mathematics (2^{nd} semester @ Science Bldg
4-506).
·
B3 Seminar (Noda, Liang)
on Introduction to Stochastic Processes.
·
B3 Seminar (Matsunuma) on Random
Walks and Electric Networks.
·
B4 Seminar (Moriya)
on Percolation.
·
B4 Seminar (Tanaka)
on Introduction to Probability Theory.
·
M1 Seminar (Kamakura)
on Markov Chains and Mixing Times.
·
M1 Seminar (Kawamoto)
on Lecture Notes on Particle Systems and
Percolation.
·
M2 Seminar (Mizushiri) on Random
Graphs and Complex Networks.
·
M2 Seminar (Nishimura)
on Introduction to Stochastic Integration.
·
D3 Seminar (Kamijima) on Quantum
effect on the divergence around the critical temperature of the Ising susceptibility.
·
CREST Seminar (Kimura, Ueda, Toyokawa) on Stability
of energy landscape.
·
CREST Seminar (Kimura, Kamijima,
Kamakura) on Stochastic cellular automata (SCA).
·
HITACHI Seminar (Kimura, Aoki, Kamijima, Ueda, Toyokawa, Ishibashi, Kamakura) @ Creative Research Institution SOUSEI.
2. Calculus I (2^{nd} semester, Tuesdays 8:45–10:15
@ Multimedia Education Bldg E-319); WeBWorK for
self-studies (need ELMS ID & Password).
3. Analysis F (2^{nd} semester, Fridays 8:45–10:15 @ Science Bldg 3-309).
4. Power-up Seminar,
FB
(September 10–13, 2019, @ National
Taisetsu Youth Friendship Center).
5. Seminar on Mathematics
(1^{st} semester @ Science Bldg 4-506).
·
B4 Seminar (Moriya)
on Percolation.
·
B4 Seminar (Naruoka) on Essence
of Probability Models.
·
B4 Seminar (Tanaka)
on Introduction to Probability Theory.
·
M1 Seminar (Kamakura)
on Markov Chains and Mixing Times.
·
M1 Seminar (Kawamoto)
on Lecture Notes on Particle Systems and
Percolation.
·
M2 Seminar (Mizushiri) on Random
Graphs and Complex Networks.
·
M2 Seminar (Nishimura)
on Introduction to Stochastic Integration.
·
D3 Seminar (Kamijima) on Quantum
effect on the divergence around the critical temperature of the Ising susceptibility.
·
PD Seminar (Chino) on
Critical properties for 1+1 dimensional oriented
percolation in a random environment.
·
CREST Seminar (Ueda, Toyokawa) on Stability
of energy landscape.
·
CREST Seminar (Kamijima,
Kamakura) on Finding optimal solutions by stochastic cellular
automata (SCA).
·
HITACHI Seminar (Aoki, Kamijima,
Ueda, Toyokawa, Ishibashi, Kamakura) @ FMI.
6. Calculus I (1^{st} semester, Mondays
10:30–12:00 @ Multimedia Education Bldg
E301; Fridays
14:45–16:15 @ Multimedia Education Bldg
E311); WeBWorK
for self-studies (need ELMS ID & Password).
Past academic years (since 2019)
· September
2015 – August 2019
Councilor of the Bernoulli Society.
· Excellent
Teachers 2018,
2015,
2012,
2011
The Hokkaido University President’s Award for Teaching Excellence in 2013 and in 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.