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Coulomb and Riesz gases: The known and the unknown
We review what is known, unknown, and expected about the mathematical properties of
Coulomb and Riesz gases. Those describe infinite configurations of points in R d interacting …
Coulomb and Riesz gases. Those describe infinite configurations of points in R d interacting …
A review of exact results for fluctuation formulas in random matrix theory
Covariances and variances of linear statistics of a point process can be written as integrals
over the truncated two-point correlation function. When the point process consists of the …
over the truncated two-point correlation function. When the point process consists of the …
Progress on the study of the Ginibre ensembles I: GinUE
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 …
Universal hidden order in amorphous cellular geometries
Partitioning space into cells with certain extreme geometrical properties is a central problem
in many fields of science and technology. Here we investigate the Quantizer problem …
in many fields of science and technology. Here we investigate the Quantizer problem …
Gaussian fluctuations and free energy expansion for Coulomb gases at any temperature
We obtain concentration estimates for the fluctuations of Coulomb gases in any dimension
and in a broad temperature regime, including very small and very large temperature regimes …
and in a broad temperature regime, including very small and very large temperature regimes …
[کتاب][B] 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 …
Ionic fluctuations in finite volumes: fractional noise and hyperuniformity
Observing finite regions of a bigger system is a common aim, from microscopy to molecular
simulations. In the latter especially, there is ongoing interest in predicting thermodynamic …
simulations. In the latter especially, there is ongoing interest in predicting thermodynamic …
Cloaking the underlying long-range order of randomly perturbed lattices
Random, uncorrelated displacements of particles on a lattice preserve the hyperuniformity of
the original lattice, that is, normalized density fluctuations vanish in the limit of infinite …
the original lattice, that is, normalized density fluctuations vanish in the limit of infinite …
The countoscope: measuring self and collective dynamics without trajectories
Driven by physical questions pertaining to quantifying particle dynamics, microscopy can
now resolve complex systems at the single-particle level, from cellular organisms to …
now resolve complex systems at the single-particle level, from cellular organisms to …
The Weyl–Heisenberg ensemble: hyperuniformity and higher Landau levels
Weyl–Heisenberg ensembles are a class of determinantal point processes associated with
the Schrödinger representation of the Heisenberg group. Hyperuniformity characterizes a …
the Schrödinger representation of the Heisenberg group. Hyperuniformity characterizes a …