Convergence in Law of the Maximum of the Two‐Dimensional Discrete Gaussian Free Field
By Maury Bramson, Jian Ding, Ofer Zeitouni. 2013
153 citations recorded by the source corpus.
We consider the discrete two‐dimensional Gaussian free field on a box of side length $N$, with Dirichlet boundary data, and prove the convergence of the law of the centered maximum of the field.© 2015 Wiley Periodicals, Inc.
Subfields: Applied Mathematics, Mathematical Physics, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/84344337c9f55e7f9f46ca23d9976cc75935a51a
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Thomas Madaule
- Joseph Najnudel
- L. Arguin
- Rishideep Roy
- Ofer Zeitouni
- Jian Ding
- David Belius
- Satya N. Majumdar
In Mathematical Physics
- Joseph Najnudel
- L. Arguin
- David Belius
- Ofer Zeitouni
- Jian Ding
- Thomas Madaule
- Rishideep Roy
- Zhan Shi
In Molecular Biology
- Thomas Madaule
- Joseph Najnudel
- L. Arguin
- David Belius
- Ofer Zeitouni
- Rishideep Roy
- G. Schehr
- Jian Ding
Citations in the corpus
- Maxima of a randomized Riemann zeta function, and branching random walks (2015, background): “[1, 2, 11], and to log-correlated Gaussian fields, see for example [10, 22].”
- On the extreme values of the Riemann zeta function on random intervals of the critical line (2016, methodology): “The discrete Gaussian Free Fields have been studied by Bramson, Ding and Zeitouni in [11] and [10].”
- Extreme value statistics of correlated random variables: A pedagogical review (2019, background): “Since then, these models have generated a lot of interest, both in physics and in mathematics, because of their relations with the extremes of the two-dimensional Gaussian Free Field (2d-GFF) [74, 243, 244].”
- Convergence of the centered maximum of log-correlated Gaussian fields (2015, methodology): “(b) Precise asymptotics for the rigth tail of the distribution of the maximum of the fine field follow from arguments similar to [7] with a number of simplifications, as our fine field has a nicer structure than its analogue in [7], whereas the coarse field employed in this paper is constant over ea”
- Maximum of a log-correlated Gaussian field (2013, methodology): “We mention that this strategy of proof is similar to that used in [1] for the BRW and also in [16] for the GFF.”
- Extrema of log-correlated random variables: Principles and Examples (2016, background): “[23] (see Biskup & Louidor [17] for the expression in terms of the derivative martingale), for a type of Gaussian Multiplicative Chaos by Madaule [50], and finally in great generality for log-correlated Gaussian fields by Ding et al.”