MITTER Pronob
Emerite CNRS
pronob.mitter
umontpellier.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

Dernieres productions scientifiques :


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.12351246 (2016)
Ref HAL: hal01338274_v1
Ref Arxiv: 1512.02877
DOI: 10.1007/s109550161507y
Ref. & Cit.: NASA ADS
Exporter : BibTex  endNote
Résumé: We prove the existence as well as regularity of a finite range decomposition for the resolvent $G_{\alpha} (xy,m^2) = ((\Delta)^{\alpha\over 2} + m^{2})^{1} (xy) $, 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 offcritical 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



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, 20150609)
Ref HAL: hal01203777_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 JonaLasinio 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 JonaLasinio's talk on our common work on large deviations for singular SPDEs.




Long Range Ferromagnets: Renormalization Group Analysis
Auteur(s): Mitter P.
(Lecture)
, 2013
Ref HAL: cel01239463_v1
Exporter : BibTex  endNote
Résumé: In this lecture I will first review rigorous results in the theory of ferromagnets with continuous spins and long range interactions on a lattice. In the long wave length approximation we get a lattice field theory of continuous spins with a nonlinear perturbation.I will then give a rigorous version of Wilson's renormalisation group to take the continuum limit as a scaling limit in a finite volume. We construct a critical theory which has a non trivial fixed point. Moreover we prove the existence of correlation functions and obtain the true scaling dimension of fields.




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.716727 (2012)
Ref HAL: hal00653859_v1
Ref Arxiv: 1112.0671
DOI: 10.1007/s109550120492z
Ref. & Cit.: NASA ADS
Exporter : BibTex  endNote
2 citations
Résumé: In (J. Stat. Phys. 115:415449, 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 selfadjoint 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



The Finite Range Renormalization Group
Auteur(s): Mitter P.
Conférence invité: The Rigorous Renormalization Group in the LHC era. (Vienne, AT, 20110920)
Ref HAL: hal00652868_v1
Exporter : BibTex  endNote
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 KadanoffWilson 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. 115,415449 (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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