IISER Kolkata ePrints Repository

Scaling Limit of Discrete Gaussian Free Fie

Nandan, Shubhamoy (2018) Scaling Limit of Discrete Gaussian Free Fie. Masters thesis, Indian Institute of Science Education and Research Kolkata.

[img] PDF (MS dissertation of Shubhamoy Nandan (13MS125)) - Submitted Version
Restricted to Repository staff only

Download (719Kb)


    In this article, we review some well-known results in the literature of random interfaces, on scaling limit of Ginzburg Landao ∇φ interfaces defined on the integer lattice Zd, to be specific. In dimension d = 1, we obtain Brownian bridge as the scaling limit of the model when considered under the effect of a uniformly strictly convex, C² potential. For dimension d ≥ 2, we consider the interface under the effect of quadratic potential which is the well-known discrete Gaussian free field. We prove that, under appropriate scaling, the discrete Gaussian free field converges to the continuous Gaussian free field. For dimension d ≥ 3, this convergence is obtained in C∞c (Rd)', the dual space of compactly supported smooth functions on Rd. While in dimension d = 2, we get the convergence in negatively indexed Sobolev spaces H₀-s 0 for s > 1.5.

    Item Type: Thesis (Masters)
    Additional Information: Supervisors: Dr. Rajat Subhra Hazra and Dr. Satyaki Mazumder
    Uncontrolled Keywords: CGFF; Continuum Gaussian Free Field; DGFF; Discrete Gaussian Free Field; Random Interfaces
    Subjects: Q Science > QA Mathematics
    Divisions: Department of Mathematics and Statistics
    Depositing User: IISER Kolkata Librarian
    Date Deposited: 06 Dec 2018 15:46
    Last Modified: 06 Dec 2018 15:46
    URI: http://eprints.iiserkol.ac.in/id/eprint/744

    Actions (login required)

    View Item