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[ Antti Kupiainen
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Antti Kupiainen
Ph.D.,
Academy Professor Group Leader
Email: firstname.lastname(at)helsinki.fi
Personal Homepage: http://mathstat.helsinki.fi/mathphys/antti.html
Telephone: +358 9 191 51460
Mailing Address: Department of Mathematics P.O.
Box 68 FIN-00014 University of Helsinki Finland
Visiting Address: Gustaf Hällströmin katu 2b,
Helsinki Room D334
My background is in Constructive Quantum Field Theory and Statistical
Mechanics. In the 80's I was developing the Renormalization Group (RG)
method for the rigorous analysis of renormalizable field theories and
phase tranistions in lattice spin systems. Some papers from this period
are numbers 1-4 appearing on the list below.
I also did some work on Conformal Field Theory. See, e.g., 5-7 below.
Subsequently I applied the RG to various problems in probability,
dynamical systems and PDE's. In the paper 8 of the list, random walk with random asymmetric
transition probabilities was shown to be diffusive in dimensions greater
than or equal to 3. In9-16, asymptotics of solutions of nonlinear parabolic PDE's
were studied using the RG in situations of decay to zero, blow-up in
finite time and formation of spatial patterns and moving fronts.
In the papers 17-20, ideas from statistical mechanics (high temperature
expansions) were used to study the Sinai-Ruelle-Bowen measures for chaotic
spatially extended dynamical systems and the problem of space-time chaos
and in 21-22, the Kolmogorov-Arnold-Moser and Melnikov theorems of
invariant tori in Hamiltonian systems were revisited using the RG.
Finally, I have been working on various aspects dealing with the
problem of turbulence. See Lessons for Turbulence, Geom. Funct. Analysis,
GAFA2000, 316-333 (2000). In 23-25 a stochastic PDE describing the advection of a scalar
quantity in a random Hölder continous velocity field was studied and
anomalous scaling and breakdown of the Kolmogorov theory of turbulence was
established. In 26 this phenomenon was shown to be connected to the
non-uniqueness of particle trajectories in turbulent velocity fields.
The question of ergodicity and uniqueness of the invariant measure for
2 dimensional stochastically forced Navier-Stokes equation was discussed
in the publications 27-29.
Publications cited aboveBack to text.
- Massless Lattice {\phi}^{4}_{4} Theory: Rigorous Control of a
Renormalizable Asymptotically Free Model, Commun. Math. Phys.
99, 197-252 (1985) (with K. Gawedzki)
- Gross-Neveu Model Through Convergent Perturbation Expansions,
Commun. Math. Phys. 102, 1-30 (1985) (with K. Gawedzki)
- Renormalization of a Non-Renormalizable Quantum Field Theory, Nucl.
Phys. B 262, 33-48 (1985) (with K. Gawedzki)
- Phase Transition in the 3d Random Field Ising model, Commun. Math.
Phys. 116, 539-572 (1987) (with J. Bricmont)
Back to text.
- The Spectrum of WZW models with Arbitrary Simple Groups, Commun.
Math. Phys. 117, 127-158 (1988) (with G. Felder, K.
Gawedzki)
- Coset Construction from Functional Integrals, Nucl. Phys.
B 320 (1989), 625-661 (with K. Gawedzki)
- SU(2) Chern-Simons Theory at Genus Zero, Commun. Math. Phys.
135, 531-554 (1990) (with K. Gawedzki)
Back to text.
- Random Walks in Asymmetric Random Environments, Commun. Math. Phys.
142, 345-420 (1991) (with J. Bricmont)
Back to text.
- Renormalization Group and Asymptotics of Solutions of Nonlinear
Parabolic Equations, Comm. Pure Appl. Math. 47, 893-922
(1994) (with J. Bricmont and G. Lin)
- Renormalization Group and the Ginzburg-Landau Equation, Commun.
Math. Phys. 150, 193-208 (1992) (with J. Bricmont)
- Renormalizing Partial Differential Equations, in Constructive
Physics, ed. by V. Rivasseau, 83-117, Springer (1995)
- Universality in Blow-up, Nonlinearity 7, 1-37
(1994) (with J. Bricmont)
- Stable Non-gaussian Diffusive Profiles, Nonlin. Analysis, Theory,
Methods and Applications, 26, 583-593 (1996) (with J.
Bricmont)
- Stability of Moving Fronts in the Ginzburg-Landau Equation, Commun.
Math. Phys. 159, 287-318 (1994) (with J. Bricmont)
- Global large time self-similarity of a thermal-diffusive combustion
system with critical nonlinearity, J. Diff Eqn, Vol. 130, No. 1, 1996,
pp 9-35 (with J. Bricmont and J. Xin)
- Stability of Cahn-Hilliard fronts, Comm. Pure Appl. Math.
52 (1999), 839-871 (with J. Bricmont, J. Taskinen)
Back to text.
- Coupled Analytic Maps, Nonlinearity 8, 379-393
(1995) (with J. Bricmont)
- High Temperature Expansions and Dynamical Systems, Commun. Math.
Phys. 178, 703-732 (1996) (with J. Bricmont)
- Infinite dimensional SRB measures, Physica D 103
(1997) 18-33 (with J. Bricmont)
- The spectrum of weakly coupled map lattices, J. Math. Pure. Appl.
77, 539-584 (1998) (with V. Baladi, M. Degli Esposti,
S. Isola, E. Järvenpää)
Back to text.
- KAM theorem and quantum field theory, Commun. Math. Phys.
201 (1999) 3, 699-727 (with J. Bricmont, K. Gawedzki)
- Renormalization
Group and the Melnikov Problem for PDE's (with J. Bricmont and A.
Schenkel)
Back to text.
- Anomalous Scaling for Passive Scalar, Phys. Rev. Lett.
75 3834 (1995) (with K. Gawedzki)
- Anomalous scaling in the N-point functions of passive scalar, Phys.
Rev. E 54, 2564 (1996) (with D. Bernard and K.
Gawedzki)
- Some mathematical problems of passive advection, Contemporary Math.
217, 83-99 (1998)
Back to text.
- Slow modes in passive advection, J. Stat. Phys. (with D. Bernard and
K. Gawedzki)
Back to text.
- Probabilistic
estimates for the two dimensional stochastic Navier-Stokes
equations, J. Stat. Phys. 100 (3/4), 2000,
743-756(with J. Bricmont, R. Lefevere)
- Ergodicity of
the 2D Navier-Stokes Equations with Random Forcing, Commun. Math.
Phys., to appear (with J. Bricmont, R. Lefevere)
- Exponential Mixing of
the 2D Stochastic Navier-Stokes Dynamics

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