• Corpus ID: 211532736

Statistical reconstruction of the Gaussian free field and KT transition

@article{Garban2020StatisticalRO,
  title={Statistical reconstruction of the Gaussian free field and KT transition},
  author={Christophe Garban and Avelio Sep'ulveda},
  journal={arXiv: Probability},
  year={2020}
}
In this paper, we focus on the following question. Assume $\phi$ is a discrete Gaussian free field (GFF) on $\Lambda \subset \frac 1 n \mathbb{Z}^2$ and that we are given $e^{iT \phi}$, or equivalently $\phi \pmod{\frac {2\pi} T}$. Can we recover the macroscopic observables of $\phi$ up to $o(1)$ precision? We prove that this statistical reconstruction problem undergoes the following Kosterlitz-Thouless type phase transition: -) If $T<T_{rec}^-$ , one can fully recover $\phi$ from the… 

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References

SHOWING 1-10 OF 48 REFERENCES

Maximum of the integer-valued Gaussian free field

We investigate the order of the maximum of the integer-valued Gaussian free field in two dimensions, and show that it grows logarithmically with the size of the box. Our treatment follows closely

Contour lines of the two-dimensional discrete Gaussian free field

We prove that the chordal contour lines of the discrete Gaussian free field converge to forms of SLE(4). Specifically, there is a constant λ > 0 such that when h is an interpolation of the discrete

Tata Lectures on Theta I

and motivation: theta functions in one variable.- Basic results on theta functions in several variables.

Logarithmic Variance for the Height Function of Square-Ice

In this article, we prove that the height function associated with the square-ice model (i.e. the six-vertex model with a=b=c=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}

Dimensions of Two-Valued Sets via Imaginary Chaos

Two-valued sets are local sets of the two-dimensional Gaussian free field (GFF) that can be thought of as representing all points of the domain that may be connected to the boundary by a curve on

Communications in Mathematical Physics

VoI.293:R.A.DeVore: The Approximation of Continous Functions by Positive Linear Operators VIII, 289 pages. 1972 DM 24,-; US $7.70 Vol.294: Stability of Stochastic Dynamical Systems Proceedings of the

The Berezinskii-Kosterlitz-Thouless Transition (Energy-Entropy Arguments and Renormalization in Defect Gases)

The study of phase transitions and of the approach to critical points in physical systems in thermal equilibrium is an important part of equilibrium statistical mechanics, but its significance goes