Coulomb Gases and Ginzburg - Landau Vortices

By Sylvia Serfaty. 2014

148 citations recorded by the source corpus.

These are the lecture notes of a "Nachdiplomvorlesung" course taught at ETH Zurich in the Spring of 2013. They appeared in the EMS series Zurich Lectures in Advanced Mathematics.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e40c43605853c557d183dfb638473497f438fd7d

How researchers see this paper

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

In Mathematical Physics

1. Xavier Ros-Oton
2. Eric Vanden-Eijnden
3. Grant M. Rotskoff
4. Nicola Abatangelo
5. Gerd Grubb
6. Enrico Valdinoci
7. M. Fall
8. Van Hoang Nguyen

In Statistics and Probability

1. Eric Vanden-Eijnden
2. Xavier Ros-Oton
3. Grant M. Rotskoff
4. Nicola Abatangelo

Citations in the corpus

• Obstacle problems for integro-differential operators: Higher regularity of free boundaries (2019, background): “More recently, such kind of obstacle problems have found applications in interacting particle systems and other related models in statistical mechanics; see [8, 29,34] and references therein.”
• Trainability and Accuracy of Artificial Neural Networks: An Interacting Particle System Approach (2018, methodology): “Using the interchangeability of the n interacting particles/parameters in the neural representation, we focus on their empirical distribution and analyze its properties when n is large using standard limit theorems [22, 23, 31, 32].”
• Neural Networks as Interacting Particle Systems: Asymptotic Convexity of the Loss Landscape and Universal Scaling of the Approximation Error (2018, methodology): “We also consider the empirical distribution of the n interacting particles / parameters and analyze the properties of this distribution when the number n is large using standard limit theorems [17, 18, 26, 27].”