Random Matrices, Random Processes and Integrable Systems

Harnad, J.

doi:10.1007/978-1-4419-9514-8

Cited by 15 publications

(2 citation statements)

References 17 publications

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“…This is interesting, since the information about the spectrum of the theory should be in principle extractable from such a representation. A paper where kernels with a similar structure are studied is [89] and a detailed review can be found in the lectures by van Moerbecke in [90]. The context of those studies is "Probability on Partitions and the Plancherel measure".…”

Section: Jhep07(2020)157mentioning

confidence: 99%

FZZT branes and non-singlets of matrix quantum mechanics

Betzios

Papadoulaki

2020

J. High Energ. Phys.

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We explore the non-singlet sector of matrix quantum mechanics dual to c = 1 Liouville theory. The non-singlets are obtained by adding N f × N bi-fundamental fields in the gauged matrix quantum mechanics model as well as a one dimensional Chern-Simons term. The present model is associated with a spin-Calogero model in the presence of an external magnetic field. In chiral variables, the low energy excitations-currents satisfy an SU(2N f)k Kǎc-Moody algebra at large N. We analyse the canonical partition function as well as two and four point correlation functions, discuss a Gross-Witten-Wadia phase transition at large N, N f and study different limits of the parameters that allow us to recover the matrix model of Kazakov-Kostov-Kutasov conjectured to describe a two dimensional black hole. The grand canonical partition function is a τ-function obeying discrete soliton equations. We finally conjecture a possible dynamical picture for the formation of a black hole in terms of condensation of long-strings in the strongly coupled region of the Liouville direction.

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Section: Jhep07(2020)157mentioning

confidence: 99%

FZZT branes and non-singlets of matrix quantum mechanics

Betzios

Papadoulaki

2020

J. High Energ. Phys.

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“…Here the sums run from µ i = 1 rather than µ = 0, because the only contribution of µ i = 0 terms to connected correlation functions is the term N x 1 of W 1 , that we wrote separately. Let us draw an example of such a discrete surface, with genus g = 2 and n = 3 holes with (µ 1 , µ 2 , µ 3 ) = (5,6,4). Marked edges are denoted by arrows which follow the orientation of the surface, so that the hole is always on the left of the arrow:…”

Section: Expectation Valuesmentioning

confidence: 99%

Random matrices

Eynard,

Kimura,

Ribault

2015

Preprint

137

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We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of algebraic geometry, loop equations and their solution using topological recursion, orthogonal polynomials and their relation with integrable systems. Each approach provides its own definition of the spectral curve, a geometric object which encodes all the properties of a model. We also introduce the two peripheral subjects of counting polygonal surfaces, and computing angular integrals.

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