Progress on the study of the Ginibre ensembles I: GinUE
SS Byun, PJ Forrester - arXiv preprint arXiv:2211.16223, 2022 - arxiv.org
The Ginibre unitary ensemble (GinUE) consists of $ N\times N $ random matrices with
independent complex standard Gaussian entries. This was introduced in 1965 by Ginbre …
independent complex standard Gaussian entries. This was introduced in 1965 by Ginbre …
Lectures on Coulomb and Riesz gases
S Serfaty - arXiv preprint arXiv:2407.21194, 2024 - arxiv.org
arXiv:2407.21194v1 [math-ph] 30 Jul 2024 Page 1 Lectures on Coulomb and Riesz Gases
Sylvia Serfaty arXiv:2407.21194v1 [math-ph] 30 Jul 2024 Page 2 Page 3 Contents Preface 5 …
Sylvia Serfaty arXiv:2407.21194v1 [math-ph] 30 Jul 2024 Page 2 Page 3 Contents Preface 5 …
From point processes to quantum optics and back
Some fifty years ago, in her seminal PhD thesis, Odile Macchi introduced permanental and
determinantal point processes. Her initial motivation was to provide models for the set of …
determinantal point processes. Her initial motivation was to provide models for the set of …
The planar low temperature Coulomb gas: separation and equidistribution
We consider planar Coulomb systems consisting of a large number n of repelling point
charges in the low temperature regime, where the inverse temperature ˇ grows at least …
charges in the low temperature regime, where the inverse temperature ˇ grows at least …
Ground states and hyperuniformity of the hierarchical Coulomb gas in all dimensions
Stochastic point processes with Coulomb interactions arise in various natural examples of
statistical mechanics, random matrices and optimization problems. Often such systems due …
statistical mechanics, random matrices and optimization problems. Often such systems due …
Progress on the Study of the Ginibre Ensembles
SS Byun, PJ Forrester - 2025 - library.oapen.org
This open access book focuses on the Ginibre ensembles that are non-Hermitian random
matrices proposed by Ginibre in 1965. Since that time, they have enjoyed prominence within …
matrices proposed by Ginibre in 1965. Since that time, they have enjoyed prominence within …
Aspects of Coulomb gases
D Chafaï - arXiv preprint arXiv:2108.10653, 2021 - arxiv.org
Coulomb gases are special probability distributions, related to potential theory, that appear
at many places in pure and applied mathematics and physics. In these short expository …
at many places in pure and applied mathematics and physics. In these short expository …
Large gap probabilities of complex and symplectic spherical ensembles with point charges
SS Byun, S Park - arXiv preprint arXiv:2405.00386, 2024 - arxiv.org
We consider $ n $ eigenvalues of complex and symplectic induced spherical ensembles,
which can be realised as two-dimensional determinantal and Pfaffian Coulomb gases on the …
which can be realised as two-dimensional determinantal and Pfaffian Coulomb gases on the …
Statistical mechanics of interpolation nodes, pluripotential theory and complex geometry
RJ Berman - arXiv preprint arXiv:1810.06939, 2018 - arxiv.org
This is mainly a survey, explaining how the probabilistic (statistical mechanical) construction
of Kahler-Einstein metrics on compact complex manifolds, introduced in a series of works by …
of Kahler-Einstein metrics on compact complex manifolds, introduced in a series of works by …