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MITTER Pronob
Emerite CNRS
pronob.mitter
univ-montp2.fr
0467144694
Bureau: 18, Etg: 1, Bât: 13 - Site : Campus Triolet
Activités de Recherche: |
Theorie quantique des champs, physique statistique et
probabilites: resultats rigoureux, groupe de renormalisation exacte. |
Domaines de Recherche: - Physique/Physique mathématique
- Physique/Matière Condensée/Mécanique statistique
- Mathématiques/Physique mathématique
- Mathématiques/Probabilités
- Physique/Physique des Hautes Energies - Phénoménologie
- Physique/Physique des Hautes Energies - Théorie
- Physique/Astrophysique
- Planète et Univers/Astrophysique
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Dernieres productions scientifiques :
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On the Convergence to the Continuum of Finite Range Lattice Covariances 
Auteur(s): Brydges David c., MITTER P.
(Article) Publié:
Journal of Statistical Physics, vol. 147 p.716-727 (2012)
Ref HAL: hal-00653859_v1
Ref Arxiv: 1112.0671
DOI: 10.1007/s10955-012-0492-z
Résumé: In (J. Stat. Phys. 115:415-449, 2004) Brydges, Guadagni and Mitter proved the existence of multiscale expansions of a class of lattice Green's functions as sums of positive definite finite range functions (called fluctuation covariances). The lattice Green's functions in the class considered are integral kernels of inverses of second order positive self-adjoint elliptic operators with constant coefficients and fractional powers thereof. The rescaled fluctuation covariance in the nth term of the expansion lives on a lattice with spacing L −n and satisfies uniform bounds. Our main result in this note is that the sequence of these terms converges in appropriate norms at a rate L −n/2 to a smooth, positive definite, finite range continuum function.
Commentaires: 14 pages
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The Finite Range Renormalization Group
Auteur(s): MITTER P.
Conférence invité: The Rigorous Renormalization Group in the LHC era. (Vienne, AT, 2011-09-20)
Ref HAL: hal-00652868_v1
Résumé: In this talk I will show that a large class of Gaussian Random Fields in the continuum or the lattice can be written as a sum of independent Gaussian random fields called fluctuation fields which enjoy the following properties: their covariances have finite range (compact support) and the fields are almost surely smooth. The fluctuation covariances satisfy very strong uniform bounds . After suitable rescaling the sequence of fluctuation fields converges in distribution to a a smooth continuum Gaussian random field whose covariance has finite range. This finite range multiscale expansion is the basis of a new mathematical form of Wilson's Renormalization Group where non local effects are minimized and estimates rendered simpler. In particular, on the lattice, this gives an alternative to the Kadanoff-Wilson renormalization group based on the block spin transformation. The talk is based on my joint work with D. Brydges and G. Guadagni (J. Stat.Phys. 115,415-449 (2004)) and a further paper with D. Brydges (2011, in preparation).
Commentaires: International Workshop at the Erwin Schroedinger International Institute for Mathematical Physics, University of Vienna.
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Self Avoiding Walks and Field Theory: Rigorous Renormalization Group Analysis.
Auteur(s): MITTER P.
Conférence invité: What is Quantum Field Theory? (Benasque, ES, 2011-09-14)
Ref HAL: hal-00656639_v1
Résumé: I give a review of some rigorous results on self avoiding walks in cubic and hypercubic lattices, including the case of self-avoiding Levy walks. I then explain the connection with supersymmetric field theory and go on to give an exposition of rigorous renormalization group analysis of the supersymmetric measure in the particular case of self avoiding Levy walks below the critical dimension. The talk is based on my joint work with D. Brydges and G. Guadagni (J.Stat.Phys. 115, 415-449 (2004), further work with D.Brydges (2011, in preparation) on finite range multiscale expansions. The renormalization group analysis of the supersymmetric measure based on the above expansions is carried out in joint work with B. Scoppola (J.Stat.Phys. 133, 921-1011 (2008)).
Commentaires: International workshop held at the Centro de Ciencias de Benasque Pedro Pascual, Benasque, Espagne
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Renormalization group analysis of a weakly self-avoiding Levy walk in the cubic lattice Z^3.
Auteur(s): Mitter P.
Conférence invité: The Renormalization Group and Statistical Mechanics (Vancouver, CA, 2009-07-06)
Ref HAL: hal-00417638_v1
Résumé: The Green's function of a weakly self-avoiding Levy walk with long range jumps in a large but finite cube in Z^3 can be expressed as the two point correlation function in a supersymmetric field theory. We have proved the global existence of the renormalization group trajectory of the underlying supersymmetric measure at all renormalization group scales . We establish the existence of the critical (stable) manifold and prove that the interactions are bounded away from zero on all scales. This is a step in a program to study rigorously the critical exponents of a self- avoiding Levy walk. Based on joint work with Benedetto Scoppola published in J.Stat Phys (2008) 133:921-1011.
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Plus...
, Scoppola B.