Matthias Allard

Matthias Allard

Researcher in Random Matrix Theory

Mathematical Physicist, engineer with a PhD specialising in Random Matrix Theory. My research focuses on universal phenomena in random matrix ensembles, including eigenvalue and singular value correlations, hard-edge asymptotics, and Coulomb gas.

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Research Interests

Random Matrix Theory Probability Complex Analysis Mathematical Physics Asymptotics Integrable Probability Coulomb Gases

Articles

Birth of a gap: Critical phenomena in 2D Coulomb gas

M. Allard and S. Lahiry.

(2025)

Link Preprint

@Article{Allard2025c,
  author        = {Matthias Allard and Sampad Lahiry},
  title         = {{Birth of a gap: Critical phenomena in 2D Coulomb gas}},
  year          = {2025},
  archiveprefix = {arXiv},
  eprint        = {2509.24529},
  primaryclass  = {math.PR},
  url           = {https://arxiv.org/abs/2509.24529},
}

Correlation functions between singular values and eigenvalues

M. Allard and M. Kieburg.

Random Matrices: Theory and Applications , 15 (01) (2025) , 2550024

DOI Link Preprint

@Article{Allard2025b,
  author        = {Allard, Matthias and Kieburg, Mario},
  journal       = {Random Matrices: Theory and Applications},
  title         = {Correlation functions between singular values and eigenvalues},
  year          = {2025},
  issn          = {2010-3263},
  number        = {01},
  pages         = {2550024},
  volume        = {15},
  archiveprefix = {arXiv},
  comment       = {doi: 10.1142/S2010326325500248},
  doi           = {10.1142/S2010326325500248},
  eprint        = {2403.19157},
  primaryclass  = {math.PR},
  publisher     = {World Scientific Publishing Co.},
  url           = {https://doi.org/10.1142/S2010326325500248},
}

Hard edge asymptotics of correlation functions between singular values and one eigenvalue

M. Allard.

Journal of Physics A: Mathematical and Theoretical , 58 (21) (2025) , 215204

DOI Link Preprint

@Article{Allard2025,
  author        = {Allard, Matthias},
  journal       = {Journal of Physics A: Mathematical and Theoretical},
  title         = {Hard edge asymptotics of correlation functions between singular values and one eigenvalue},
  year          = {2025},
  issn          = {1751-8113},
  number        = {21},
  pages         = {215204},
  volume        = {58},
  archiveprefix = {arXiv},
  doi           = {10.1088/1751-8121/add9f3},
  eprint        = {2501.15765},
  primaryclass  = {math.PR},
  publisher     = {IOP Publishing},
  url           = {https://dx.doi.org/10.1088/1751-8121/add9f3},
}

Partition function of 2D Coulomb gases with radially symmetric potentials and a hard wall

M. Allard, P. J. Forrester, S. Lahiry, and B. Shen.

(2025)

Link Preprint

@Article{Allard2025a,
  author        = {Matthias Allard and Peter J. Forrester and Sampad Lahiry and Bojian Shen},
  title         = {Partition function of {2D} {C}oulomb gases with radially symmetric potentials and a hard wall},
  year          = {2025},
  archiveprefix = {arXiv},
  eprint        = {2506.14738},
  primaryclass  = {math.PR},
  url           = {https://arxiv.org/abs/2506.14738},
}

Correlation functions between eigenvalues and singular values

M. Allard.

PhD thesis, University of Melbourne & KU Leuven (2025).

PDF

@phdthesis{Allard2025PhD,
    author = {Allard, Matthias},
    title = {Correlation functions between eigenvalues and singular values},
    school = {University of {M}elbourne \& {L}euven},
    year = {2025},
    }

Experience

Tutor

University of Melbourne

2023 – 2026

Teaching responsibilities included:

Calculus 1
Calculus 2
Linear Algebra
Physics laboratories

Tutor

KU Leuven

2021 – 2022

Teaching responsibilities included:

Calculus 1
Differential Equations

Research Project

Imperial College London

2020 – 2020

Topics included:

Directed Acyclic Graphs
Minkowski distances
Percolation models

Research Engineering Intern

Thales Alenia Space

2019 – 2019

Responsibilities included:

Model optical fiber components within an imaging spectrometer
Conduct calibration and modeling of an imaging Fourier-transform spectrometer
Study speckle phenomena and optical signal processing

Engineering Project

Institut d'Optique Graduate School

2018 – 2019

Responsibilities included:

Design and implement an industrial vision system
Work on programming, mechanical engineering, and electrical engineering components

Research Intern

Observatoire des Hauts de Provence

2018 – 2018

Topics included:

Image processing
Speckle analysis
Infrared detectors
Astronomical observations

Sports Activities Coordinator

Institut d'Optique Graduate School

2018 – 2019

Responsibilities included:

Organize events
Coordinate teams
Plan student activities

Education

Joint PhD in Random Matrices and Complex Analysis

University of Melbourne & KU Leuven

2021 – 2025

Joint PhD under the supervision of Mario Kieburg (University of Melbourne) and Arno Kuijlaars (KU Leuven).

Research topics included:

Random Matrix Theory
Probability
Harmonic Analysis
Orthogonal Polynomials
Measure Theory
Coulomb Gases

Read Thesis

MSc Physics (Double Diploma), with Distinction

Imperial College London

2019 – 2020

Courses included:

Quantum Information
Quantum Field Theory
Unification
General Relativity
Mathematical Methods for Physicists
Plasmonics and Metamaterials
Group Theory

Diplôme d'Ingénieur Photonics & MSc Fundamental Physics

Institut d'Optique Graduate School & Université Paris-Saclay

2018 – 2019

Concurrent engineering and physics degrees.

Courses included:

Fourier Optics
Nonlinear Optics
Radiometry
Optical System Design
Light-Matter Interaction
Atomic Physics
Plasma Physics
Particle Physics

Diplôme d'Ingénieur Photonics & BSc Fundamental Physics

Institut d'Optique Graduate School & Université Paris-Saclay

2017 – 2018

Concurrent engineering and physics degrees.

Courses included:

Signal Processing
Polarization
Laser Physics
Scientific Computing
Optical Physics
Quantum Physics
Statistical Physics
Special Relativity
Analytical Mechanics
Electromagnetism

Classe Préparatoire aux Grandes Écoles

Lycée Chaptal

2015 – 2017

Two-year intensive undergraduate preparation in:

Mathematics (14h/week)
Physics (12h/week)
Engineering (12h/week)

No results found

Researcher in Random Matrix Theory

Research Interests

Experience

Tutor

Tutor

Research Project

Research Engineering Intern

Engineering Project

Research Intern

Sports Activities Coordinator

Education

Joint PhD in Random Matrices and Complex Analysis

MSc Physics (Double Diploma), with Distinction

Diplôme d'Ingénieur Photonics & MSc Fundamental Physics

Diplôme d'Ingénieur Photonics & BSc Fundamental Physics

Classe Préparatoire aux Grandes Écoles