Log-Gases and Random Matrices

By Peter J. Forrester. 2010

1,559 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b17927dad09bdfd1c1ab8cd9ed4219dc13fc741c

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Citations in the corpus

• The Crystallization Conjecture: A Review (2015, methodology): “e eigenvalues is given by the measure σ solution to the minimization problem in (41). The next order is more complex and its link with the crystal problem is less clear [72]. We refer for instance to [174, 92, 13] for a detailed study of the subject. 3.2. Several types of particles. In order to deal”
• The Surprising Mathematics of Longest Increasing Subsequences (2015, unknown): “For extensive information about applications of orthogonal polynomials to random matrix theory, see [4], [30], [42], [88].”
• On Combinatorial Expansion of the Conformal Blocks Arising from AGT Conjecture (2010, methodology): “(12)We note that the method suggested in [51] is a generalization of Anderson’s derivation of Selberg integral [52] (see also [53]).”
• Top eigenvalue of a random matrix: large deviations and third order phase transition (2013, background): “The joint probability density function (PDF) of these eigenvalues is given by the classical result [2, 3, 11] Pjoint(λ1, λ2, · · · , λN) = BN exp [”
• Higher‐Dimensional Coulomb Gases and Renormalized Energy Functionals (2013, background): “xists between “log-gases” in dimension 1 and the GUE and GOE ensembles of random matrices, as well as more indirectly to orthogonal polynomial ensembles. For more details on these aspects we refer to [For], and for an introduction to the random matrix aspect to the texts [AGZ, Meh, Dei]. A recent tr”
• Small deviations for beta ensembles (2009, background): “Importantly, off of β = 1, 2, 4, despite considerable efforts (see [9], Chapter 13 for a comprehensive review), there appears to be no characterization of the correlation functions amenable to asymptotics.”
• Approximation of Haar distributed matrices and limiting distributions of eigenvalues of Jacobi ensembles (2009, methodology): “A good reference for random matrix theory and applications in Physics are Beenakker [11], Bohigas [12], Forrester [ 30 ], Guhr [35] and Mehta [54].”
• Multidimensional Yamada-Watanabe theorem and its applications to particle systems (2011, methodology): “For more information on log-gases, see the recent monograph of Forrester [11].”
• How instanton combinatorics solves Painlevé VI, V and IIIs (2013, background): “For φ, ψ given by classical special functions and sufficiently simple I, this system can often be solved in terms of Painlevé functions [23, 35, 54, 55, 56, 59].”
• Accuracy of the Tracy–Widom limits for the extreme eigenvalues in white Wishart matrices (2012, methodology): “ion and yields a very natural integral representation for the correlation kernel which later appears in the central formula Eq.(50) there; see Johnstone (2007, Section 2.2, also Eq.’s (16) and (46)), Forrester (2004, Proposition 4.11) and Adler et al. (2000, Proposition 4.2). Following Forrester (20”
• Universality for generalized Wigner matrices with Bernoulli distribution (2010, methodology): “The formulas for the GOE cases are more complicated and we refer the reader to standard references such as [1, 6, 20, 24].”
• Coulomb Gases and Ginzburg - Landau Vortices (2014, methodology): “This is usually called a log gas, and its motivation also comes from Random Matrix Theory (see [Fo]): one-dimensional counterparts to the Ginibre ensemble are the Gaussian Unitary Ensemble (GUE) and the Gaussian Orthogonal Ensemble (GOE), which are symmetric analogues of it.”
• Random matrix theory in statistics: A review (2014, background): “More complete and self-containing treatments of a number of “core” topics of RMT not covered in this paper, including the Riemann–Hilbert approach to the asymptotics of orthogonal polynomials and random matrices, the distribution of spacings and correlation functions of eigenvalues and their connect”