Renormalization Group and Stochastic PDEs

Antti Kupiainen1
1Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014, Helsinki, Finland

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Tài liệu tham khảo

Hairer, M.: A theory of regularity structures. Invent. Math. (2014). doi: 10.1007/s00222-014-0505-4

Catellier, R., Chouk, K.: Paracontrolled distributions and the 3-dimensional stochastic quantization equation. (2013), 2. arXiv:1310.6869 [math-ph]

Gubinelli, M., Imkeller, P., Perkowski, N.: Paracontrolled distributions and singular PDEs. (2012) arXiv:1210.2684

Wilson, K.: http://www.nobelprize.org/nobelprizes/physics/laureates/1982/wilson-lecture

Bricmont J., Kupiainen A., Lin G.: Renormalization group and asymptotics of solutions of nonlinear parabolic equations. Commun. Pure. Appl. Math. 47, 893–922 (1994)

Bricmont J., Gawedzki K., Kupiainen A.: KAM theorem and quantum field theory. Commun. Math. Phys. 201(3), 699–727 (1999)

Unterberger, J.: Diffusive limit for 3-dimensional KPZ equation. (2) Generalized PDE estimates through Hamilton–Jacobi–Bellman formalism. arXiv:1312.5293 [math.AP]

Glimm J.: Boson fields with the $${:\phi^4:}$$ : ϕ 4 : interaction in three dimensions. Commun. Math. Phys. 10, 1–47 (1968)

Eckmann J.-P., Ostervalder K.: On the uniqueness of the Hamiltionian and of the representation of the CCR for the quartic boson interaction in three dimensions. Helv. Phys. Acta 44, 884–909 (1971)

Glimm J., Jaffe A.: Positivity of the $${\phi_3^4}$$ ϕ 3 4 Hamiltonian. Fortschr. Physik 21, 327–376 (1973)

Feldman J.: The $${\lambda\phi^4_3}$$ λ ϕ 3 4 field theory in a finite volume. Commun. Math. Phys. 37, 93–120 (1974)

Feldman J.S., Ostervalder K.: The Wightman axioms and the mass gap for weakly coupled $${\phi^4_3}$$ ϕ 3 4 quantum field theories. Ann. Phys. 97(1), 80–135 (1976)

Bogachev V.I.: Gaussian Measures (Mathematical Surveys and Monographs). American Mathematical Society, Providence (1998)

Nualart D.: The Malliavin calculus and related topics. Probability and its Applications (New York), second ed. Springer, Berlin (2006)