Gaussian asymptotics of discrete β $\beta $ -ensembles

Borodin, Alexei; Gorin, Vadim; Guionnet, Alice

doi:10.1007/s10240-016-0085-5

Cited by 54 publications

(177 citation statements)

References 55 publications

Supporting

Mentioning

175

Contrasting

Order By: Relevance

“…(1) The horizontal lozenges along the section x = t form a discrete log-gas (this was shown in [BGG,Section 9.2]), and therefore, LLN and CLT for them follows from the results of [BGG]. (2) We show how the covariance in CLT of [BGG,Theorem 7.1] can be used to construct the covariance function for the Gaussian Free Field.…”

Section: 4mentioning

confidence: 90%

Fourier transform on high-dimensional unitary groups with applications to random tilings

Bufetov¹,

Gorin²

2019

Duke Math. J.

Self Cite

View full text Add to dashboard Cite

A combination of direct and inverse Fourier transforms on the unitary group U (N ) identifies normalized characters with probability measures on N -tuples of integers. We develop the N → ∞ version of this correspondence by matching the asymptotics of partial derivatives at the identity of logarithm of characters with Law of Large Numbers and Central Limit Theorem for global behavior of corresponding random N -tuples.As one application we study fluctuations of the height function of random domino and lozenge tilings of a rich class of domains. In this direction we prove the Kenyon-Okounkov's conjecture (which predicts asymptotic Gaussianity and exact form of the covariance) for a family of non-simply connected polygons.Another application is a central limit theorem for the U (N ) quantum random walk with random initial data.

show abstract

Section: 4mentioning

confidence: 90%

Fourier transform on high-dimensional unitary groups with applications to random tilings

Bufetov¹,

Gorin²

2019

Duke Math. J.

Self Cite

View full text Add to dashboard Cite

show abstract

“…We also get a new perspective on the rôle of Whitham hierarchies [46,63] and their quantum and qq-deformations in gauge theory. See also [13] for more applications of qq-characters in the U(1) case.…”

Section: Jhep03(2016)181mentioning

confidence: 99%

BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters

Nekrasov

2016

J. High Energ. Phys.

213

466

View full text Add to dashboard Cite

We study symmetries of quantum field theories involving topologically distinct sectors of the field space. To exhibit these symmetries we define special gauge invariant observables, which we call the qq-characters. In the context of the BPS/CFT correspondence, using these observables, we derive an infinite set of Dyson-Schwinger-type relations. These relations imply that the supersymmetric partition functions in the presence of Ω-deformation and defects obey the Ward identities of two dimensional conformal field theory and its q-deformations. The details will be discussed in the companion papers.

show abstract

“…Specifically in this context I would like to mention certain discrete versions of the Schwinger-Dyson equation developed by Nekrasov [32]; see also earlier papers by Nekrasov and his collaborators [34,35]. The paper [3] is a perfect demonstration of the force of such methods in probabilistic applications.…”

Section: M(r C) ⊃ M(r C)mentioning

confidence: 99%