MITTER Pronob
Fonction : Directeur de Recherche Émérite
Emerite CNRS
pronob.mitter
umontpellier.fr
Bureau: 18, Etg: 1, Bât: 13 - Site : Campus Triolet
Activités de Recherche: |
| Quantum Field Theory, Statistical Physics and Probability: rigorous results, exact renormalization group, stochastic quantization. |
Domaines de Recherche: - Physique/Physique mathématique
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Dernieres productions scientifiques :
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Introduction to the Renormalization group. 
Auteur(s): Mitter P.
Conférence invité: Scaling limits, rough paths, quantum field theory (Cambridge, GB, 2018-09-03)
Texte intégral en Openaccess : 
Ref HAL: hal-01935444_v2
Exporter : BibTex | endNote
Résumé: In these lectures I will introduce and explore properties of the Renormalisation Group (RG) both in its discrete and continuous forms. Topics to be discussed include multi scale expansions, the RG, Gaussian fixed points, Wick products from the RG point of view, ultraviolet cutoff removal, flow equations and perturbative flows, trivial and non-trivial fixed points, and critical field theories. Rigorous Discrete RG analysis. I will discuss a rigorous application for a non-trivial fixed point.
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On a Finite Range Decomposition of the Resolvent of a Fractional Power of the Laplacian II. The Torus
Auteur(s): Mitter P.
(Article) Publié:
Journal Of Statistical Physics, vol. 168 p.986-999 (2017)
Texte intégral en Openaccess : 
Ref HAL: hal-01492858_v1
Ref Arxiv: 1701.04111
DOI: 10.1007/s10955-017-1828-5
WoS: WOS:000407382100003
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
3 Citations
Résumé: In previous papers, [M1, M2], [M3], we proved the existence as well as regularity of a finite range decomposition for the resolvent $G_{\alpha} (x-y,m^2) = ((-\Delta)^{\alpha\over 2} + m^{2})^{-1} (x-y) $, for $0<\alpha <2$ and all real $m$, in the lattice ${\bf Z}^{d}$ for dimension $d\ge 2$. In this paper, which is a continuation of the previous one, we extend those results by proving the existence as well as regularity of a finite range decomposition for the same resolvent but now on the lattice torus ${\bf Z}^{d}/L^{N+1}{\bf Z}^{d} $ for $d\ge 2$ provided $m\neq 0$ and $0<\alpha <2$. We also prove differentiability and uniform continuity properties with respect to the resolvent parameter $m^{2}$. Here $L$ is any odd positive integer and $N\ge 2$ is any positive integer.
Commentaires: 17 pages
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On a Finite Range Decomposition of the Resolvent of a Fractional Power of the Laplacian (vol 163, pg 1235, 2016)
Auteur(s): Mitter P.
(Article) Publié:
Journal Of Statistical Physics, vol. 166 p.453-455 (2017)
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On a Finite Range Decomposition of the Resolvent of a Fractional Power of the Laplacian
Auteur(s): Mitter P.
(Article) Publié:
Journal Of Statistical Physics, vol. 163 p.1235-1246 (2016)
Texte intégral en Openaccess :
Ref HAL: hal-01338274_v1
Ref Arxiv: 1512.02877
DOI: 10.1007/s10955-016-1507-y
WoS: WOS:000375579300009
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
3 Citations
Résumé: We prove the existence as well as regularity of a finite range decomposition for the resolvent $G_{\alpha} (x-y,m^2) = ((-\Delta)^{\alpha\over 2} + m^{2})^{-1} (x-y) $, for $0<\alpha<2$ and all real $m$, in the lattice ${\mathbf Z}^{d}$ as well as in the continuum ${\mathbf R}^{d}$ for dimension $d\ge 2$. This resolvent occurs as the covariance of the Gaussian measure underlying weakly self- avoiding walks with long range jumps (stable L\'evy walks) as well as continuous spin ferromagnets with long range interactions in the long wavelength or field theoretic approximation. The finite range decomposition should be useful for the rigorous analysis of both critical and off-critical renormalisation group trajectories. The decomposition for the special case $m=0$ was known and used earlier in the renormalisation group analysis of critical trajectories for the above models below the critical dimension $d_c =2\alpha$.
Commentaires: 16 pages, 1 figure, typos corrected, corrected, reference added, one sentence added
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Singular Stochastic PDEs and Dynamical Field Theory Models.
Auteur(s): Mitter P.
Conférence invité: Constructive Renormalisation Group: A Conference in honour of Pierluigi Falco. (Frascati, IT, 2015-06-09)
Texte intégral en Openaccess :
Ref HAL: hal-01203777_v1
Exporter : BibTex | endNote
Résumé: There is considerable interest at present in Singular Stochastic PDEs especially in connection with rough path theory in different guises. The mathematical work started with results by Giovanni Jona-Lasinio and myself a long time ago. I will review what was accomplished at the time and the progress that has been made since then. One reason for presenting this to this audience is that there is, in my opinion, considerable scope for rigorous renormalsation group work in this subject as I will explain. I will also attempt to prepare the ground for Jona-Lasinio's talk on our common work on large deviations for singular SPDEs.
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