Extreme values for two-dimensional discrete Gaussian free field

By Jian Ding, Ofer Zeitouni. 2012

50 citations recorded by the source corpus.

We consider in this paper the collection of near maxima of the discrete, two dimensional Gaussian free field in a box with Dirichlet boundary conditions. We provide a rough description of the geometry of the set of near maxima, estimates on the gap between the two largest maxima, and an estimate for the right tail up to a multiplicative constant on the law of the centered maximum.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fe5f443b4438fb0a77fb245ea88b8f27bf7e71e4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Ofer Zeitouni
2. L. Arguin
3. Maury Bramson
4. Jian Ding
5. David Belius
6. Rishideep Roy
7. P. Bourgade
8. Zhan Shi

In Mathematical Physics

1. Ofer Zeitouni
2. L. Arguin
3. David Belius
4. Jian Ding
5. Joseph Najnudel
6. N. Kistler
7. Zhan Shi
8. Rishideep Roy

Citations in the corpus

• Convergence of the centered maximum of log-correlated Gaussian fields (2015, methodology): “In order to see that, note that, by Theorem 1.2, where O (1) is an error term independent of all parameters. n addition, by considering a N/ 2 -box in the left side and dividing the right half box into two copies of N/ 2 -boxes, one gets that where ∗ ∗ 1 and v ∗ 2 are the maximizers of the DGFF in t”
• Convergence in law of the maximum of nonlattice branching random walk (2014, methodology): “Our proof of Theorem 1.1 is, we believe, shorter and more elementary than that in [2], employing techniques developed in Ding and Zeitouni [8] and Bramson, Ding, and Zeitouni [5].”
• The extremal process of branching Brownian motion (2011, background): “8) (after this paper has been submitted, partial progress towards this conjecture has been achieved in [27], and [28]).”
• Convergence in Law of the Maximum of the Two‐Dimensional Discrete Gaussian Free Field (2013, methodology): “Aspects of this model have been treated in both the mathematics and physics literature; we refer the reader to [15] for an extensive discussion of the history of this problem.”
• Maximum of the Characteristic Polynomial of Random Unitary Matrices (2015, background): “In a series of impressive work, the form of the subleading correction as well as convergence of the fluctuations have been obtained [11, 16, 19, 32].”