Accueil >
Production scientifique
(17) Production(s) de MITTER P.
|
|
The Exact Renormalization Group 
Auteur(s): Mitter P.
Chapître d'ouvrage: Encyclopedia Of Mathematical Physics, vol. p.17 pages (2006)
Texte intégral en Openaccess : 
Ref HAL: in2p3-00024177_v1
Ref Arxiv: math-ph/0505008
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé: This is a very brief introduction to Wilson's Renormalization Group with emphasis on mathematical developments.
Commentaires: 17 pages, AMS LaTeX. Contribution to the Encyclopedia of Mathematical Physics (Elsevier, 2006) - MSC-class: 81T08; 82B05; 37D20
|
|
|
|
Finite Range Decomposition of Gaussian Processes
Auteur(s): Mitter P. , Brydges David, Guadagni G.
(Article) Publié:
Journal Of Statistical Physics, vol. 115 p.415-449 (2004)
Texte intégral en Openaccess :
Ref HAL: hal-00286525_v1
Ref Arxiv: math-ph/0303013
DOI: 10.1023/B:JOSS.0000019818.81237.66
WoS: 000220250600020
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
33 Citations
Résumé: Let Delta be the finite difference Laplacian associated to the lattice Z d . For dimension dge3, age0, and L a sufficiently large positive dyadic integer, we prove that the integral kernel of the resolvent G a colone(a–Delta)–1 can be decomposed as an infinite sum of positive semi-definite functions V n of finite range, V n (x–y)=0 for |x–y|geO(L) n . Equivalently, the Gaussian process on the lattice with covariance G a admits a decomposition into independent Gaussian processes with finite range covariances. For a=0, V n has a limiting scaling form $$L^{ - n\left( {d - 2} \right)} \Gamma _{c,*} \left( {\tfrac{{x - y}}{{L^n }}} \right)$$ as nrarrinfin. As a corollary, such decompositions also exist for fractional powers (–Delta)–agr/2, 0
Commentaires: 26 pages, LaTeX, paper in honour of G.Jona-Lasinio.Typos corrected, corrections in section 5 and appendix A
|
|
|
|
CRITICAL (Phi^{4}_{3,\epsilon})
Auteur(s): Brydges D. C., Mitter P., Scoppola B.
(Article) Publié:
Communications In Mathematical Physics, vol. 240 p.281-327 (2003)
Texte intégral en Openaccess :
Ref HAL: hal-00176682_v1
Ref Arxiv: hep-th/0206040
DOI: 10.1007/s00220-003-0895-4
WoS: 000185597800012
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
37 Citations
Résumé: The Euclidean $(\phi^{4})_{3,\epsilon$ model in $R^3$ corresponds to a perturbation by a $\phi^4$ interaction of a Gaussian measure on scalar fields with a covariance depending on a real parameter $\epsilon$ in the range $0\le \epsilon \le 1$. For $\epsilon =1$ one recovers the covariance of a massless scalar field in $R^3$. For $\epsilon =0$ $\phi^{4}$ is a marginal interaction. For $0\le \epsilon < 1$ the covariance continues to be Osterwalder-Schrader and pointwise positive. After introducing cutoffs we prove that for $\epsilon > 0$, sufficiently small, there exists a non-gaussian fixed point (with one unstable direction) of the Renormalization Group iterations. These iterations converge to the fixed point on its stable (critical) manifold which is constructed.
Commentaires: 49 pages, plain tex, macros included
|
