Luca Guido Molinari | Università degli Studi di Milano - State University of Milan (Italy) (original) (raw)
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Papers by Luca Guido Molinari
Journal of Physics A: Mathematical and General, 1990
ABSTRACT The authors provide the general solution of the large-N limit of matrix models with even... more ABSTRACT The authors provide the general solution of the large-N limit of matrix models with even polynomial potential in the phase with two minimal. The solution is given both in the saddle point and in the orthogonal polynomials approaches.
arXiv (Cornell University), Oct 12, 2022
Journal of Mathematical Physics, May 1, 2019
Acta Mathematica Hungarica, May 18, 2016
Mathematics, May 18, 2022
Journal of physics, Feb 1, 1987
A two-parameter model of Hermitian matrices in zero-dimensional space is solved in the large-N li... more A two-parameter model of Hermitian matrices in zero-dimensional space is solved in the large-N limit. A very interesting phase diagram and a spontaneous magnetisation are exhibited.
Journal of physics, May 7, 1990
The simplest matrix model which exhibits multicritical points is carefully analysed. The authors ... more The simplest matrix model which exhibits multicritical points is carefully analysed. The authors reproduce results of potential interest for the non-perturbative theory of strings in the region where the orthogonal polynomials were correctly used. However, the analysis holds for the whole parameter space.
arXiv (Cornell University), Sep 23, 2014
arXiv (Cornell University), Jan 4, 2018
arXiv (Cornell University), Feb 5, 2008
arXiv (Cornell University), Aug 13, 2023
arXiv (Cornell University), Jun 9, 2023
General Relativity and Gravitation, Apr 1, 2023
Fundamental Journal of Mathematics and Applications
I reconsider the approximation of Bessel functions with finite sums of trigonometric functions, i... more I reconsider the approximation of Bessel functions with finite sums of trigonometric functions, in the light of recent evaluations of Neumann-Bessel series with trigonometric coefficients. A proper choice of angle allows for an efficient choice of the trigonometric sum. Based on these series, I also obtain straightforward non-standard evaluations of new parametric sums with powers of cosine and sine functions.
arXiv: Mathematical Physics, 2018
We extend to twisted space-times the following property of Generalized Robertson-Walker spacetime... more We extend to twisted space-times the following property of Generalized Robertson-Walker spacetimes: the Weyl tensor is divergence-free if and only if its contraction with the time-like unit torse-forming vector is zero. Despite the simplicity of the statement, the proof is involved. As a product of the same calculation, we introduce a new generalized curvature tensor, with an interesting recurrence property.
Colloquium Mathematicum, 2022
The Oxford Handbook of Random Matrix Theory, 2018
This article considers phase transitions in matrix models that are invariant under a symmetry gro... more This article considers phase transitions in matrix models that are invariant under a symmetry group as well as those that occur in some matrix ensembles with preferred basis, like the Anderson transition. It first reviews the results for the simplest model with a nontrivial set of phases, the one-matrix Hermitian model with polynomial potential. It then presents a view of the several solutions of the saddle point equation. It also describes circular models and their Cayley transform to Hermitian models, along with fixed trace models. A brief overview of models with normal, chiral, Wishart, and rectangular matrices is provided. The article concludes with a discussion of the curious single-ring theorem, the successful use of multi-matrix models in describing phase transitions of classical statistical models on fluctuating two-dimensional surfaces, and the delocalization transition for the Anderson, Hatano-Nelson, and Euclidean random matrix models.
Journal of Mathematical Physics, 1987
Models with a multiplet of field variables arranged into rectangular matrices, in the limit of in... more Models with a multiplet of field variables arranged into rectangular matrices, in the limit of infinite dimensions of the matrices, are studied. In zero-dimensional space (where the problem is a combinatorial one) a closed solution is given that improves the one previously known. In arbitrary space dimension a symmetry is described that connects rectangular models with vector models.
Journal of Physics A: Mathematical and General, 1990
ABSTRACT The authors provide the general solution of the large-N limit of matrix models with even... more ABSTRACT The authors provide the general solution of the large-N limit of matrix models with even polynomial potential in the phase with two minimal. The solution is given both in the saddle point and in the orthogonal polynomials approaches.
arXiv (Cornell University), Oct 12, 2022
Journal of Mathematical Physics, May 1, 2019
Acta Mathematica Hungarica, May 18, 2016
Mathematics, May 18, 2022
Journal of physics, Feb 1, 1987
A two-parameter model of Hermitian matrices in zero-dimensional space is solved in the large-N li... more A two-parameter model of Hermitian matrices in zero-dimensional space is solved in the large-N limit. A very interesting phase diagram and a spontaneous magnetisation are exhibited.
Journal of physics, May 7, 1990
The simplest matrix model which exhibits multicritical points is carefully analysed. The authors ... more The simplest matrix model which exhibits multicritical points is carefully analysed. The authors reproduce results of potential interest for the non-perturbative theory of strings in the region where the orthogonal polynomials were correctly used. However, the analysis holds for the whole parameter space.
arXiv (Cornell University), Sep 23, 2014
arXiv (Cornell University), Jan 4, 2018
arXiv (Cornell University), Feb 5, 2008
arXiv (Cornell University), Aug 13, 2023
arXiv (Cornell University), Jun 9, 2023
General Relativity and Gravitation, Apr 1, 2023
Fundamental Journal of Mathematics and Applications
I reconsider the approximation of Bessel functions with finite sums of trigonometric functions, i... more I reconsider the approximation of Bessel functions with finite sums of trigonometric functions, in the light of recent evaluations of Neumann-Bessel series with trigonometric coefficients. A proper choice of angle allows for an efficient choice of the trigonometric sum. Based on these series, I also obtain straightforward non-standard evaluations of new parametric sums with powers of cosine and sine functions.
arXiv: Mathematical Physics, 2018
We extend to twisted space-times the following property of Generalized Robertson-Walker spacetime... more We extend to twisted space-times the following property of Generalized Robertson-Walker spacetimes: the Weyl tensor is divergence-free if and only if its contraction with the time-like unit torse-forming vector is zero. Despite the simplicity of the statement, the proof is involved. As a product of the same calculation, we introduce a new generalized curvature tensor, with an interesting recurrence property.
Colloquium Mathematicum, 2022
The Oxford Handbook of Random Matrix Theory, 2018
This article considers phase transitions in matrix models that are invariant under a symmetry gro... more This article considers phase transitions in matrix models that are invariant under a symmetry group as well as those that occur in some matrix ensembles with preferred basis, like the Anderson transition. It first reviews the results for the simplest model with a nontrivial set of phases, the one-matrix Hermitian model with polynomial potential. It then presents a view of the several solutions of the saddle point equation. It also describes circular models and their Cayley transform to Hermitian models, along with fixed trace models. A brief overview of models with normal, chiral, Wishart, and rectangular matrices is provided. The article concludes with a discussion of the curious single-ring theorem, the successful use of multi-matrix models in describing phase transitions of classical statistical models on fluctuating two-dimensional surfaces, and the delocalization transition for the Anderson, Hatano-Nelson, and Euclidean random matrix models.
Journal of Mathematical Physics, 1987
Models with a multiplet of field variables arranged into rectangular matrices, in the limit of in... more Models with a multiplet of field variables arranged into rectangular matrices, in the limit of infinite dimensions of the matrices, are studied. In zero-dimensional space (where the problem is a combinatorial one) a closed solution is given that improves the one previously known. In arbitrary space dimension a symmetry is described that connects rectangular models with vector models.