Entropic repulsion and the maximum of the two-dimensional harmonic crystal

By E. Bolthausen, Jean-Dominique Deuschel, Giambattista Giacomin. 2001

200 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/411d8f59c542e619392b8515ab624707341ee19c

How researchers see this paper

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

In Computational Theory and Mathematics

1. P. Bourgade
2. Jian Ding
3. Ofer Zeitouni
4. David Belius
5. Zhan Shi
6. Joseph Najnudel
7. L. Arguin

In Mathematical Physics

1. Joseph Najnudel
2. Zhan Shi
3. L. Arguin
4. Thomas Madaule
5. David Belius
6. Ofer Zeitouni
7. Jian Ding
8. P. Bourgade

Citations in the corpus

• Asymptotics of cover times via Gaussian free fields: Bounded-degree graphs and general trees (2011, methodology): “For the 2D lattice, the asymptotics of the supremum of the Gaussian free field was determined in [9], and the asymptotics of cover times was established in [16].”
• Branching random walks (2015, result): “By comparison to analoguous results for branching random walks, many deep results have been recently established for Gaussian free fields and more general logarithmically correlated Gaussian fields (Bolthausen, Deuschel and Giacomin [61], Madaule [183], Biskup and Louidor [60], Ding, Roy and Zeitoun”
• Maximum of the Characteristic Polynomial of Random Unitary Matrices (2015, background): “In mathematics, the leading order of the twodimensional Gaussian Free Field, was determined in [12].”
• Convergence in Law of the Maximum of the Two‐Dimensional Discrete Gaussian Free Field (2013, background): “Of greatest relevance to this paper are the papers [5], where it is proved that N =.”
• Extrema of log-correlated random variables: Principles and Examples (2016, methodology): “The analogue for the 2DGFF was proved by Bolthausen, Deuschel & Giacomin [18].”
• Stochastic Interface Models (2005, background): “[28] and Daviaud [60] studied the fine behavior of maxx φ(x) for d = 2 for Gaussian case.”
• Localization and delocalization of random interfaces (2005, background): “It is proved in [16] that the maximum of the 2-dimensional finite-range Gaussian field in the box ΛN satisfies, for any δ > 0,”
• Extreme values for two-dimensional discrete Gaussian free field (2012, background): “The first natural “comparable” process is the branching random walk (BRW) which admits a natural tree structure (although [12] do not use directly Gaussian comparisons, the BRW features implicitly in their approach).”
• Tightness of the recentered maximum of the two‐dimensional discrete Gaussian free field (2010, background): “king similarity with the behavior of branching random walks (BRW), see [Br78] (where branching Brownian motions are considered) and [ABR09]. The relation with (an imbedded) BRW is already apparent in [BDG01], but the argument there is not sharp enough to allow for a control of the logn term in (1.1)”
• On the extreme values of the Riemann zeta function on random intervals of the critical line (2016, methodology): “The general principle of this method can be found in the lecture notes by Kistler [22], and its spirit goes back to the work by Bolthausen, Deuschel and Giacomin [6], in their study of the extreme values of the two-dimensional Gaussian free field.”
• Maximum of a log-correlated Gaussian field (2013, background): “Let us mention that in the discrete setting, Z2 ∩ [0,N ]2, if we add the zero boundary condition, the model becomes the so-called Gaussian free field (GFF), which has attracted many recent attentions, see [15], [14] and [17].”