Publications in Mathematical Physics and Probability:

All my publications are available on arXiv, or ResearchGate. My orcid number is "0000-0003-0306-8943" . Below is a list of some of them:

  1. Explicit Hamiltonian representations of meromorphic connections and duality from different perspectives: a case study, M. Alameddine, O. Marchal [arXiv:2406.19187], 2024.
  2. Hearing the shape of an arena with spectral swarm robotics, L. Cazenille, N. Lobato-Dauzier, A. Loi, M. Ito, O. Marchal, N. Aubert-Kato, N. Bredeche, A.J. Genot [arXiv:2403.17147], 2024.
  3. Optimal sub-Gaussian variance proxy for truncated Gaussian and exponential random variables, M. Barreto, O. Marchal, J. Arbel [arXiv:2403.08628], 2024.
  4. Isomonodromic and isospectral deformations of meromorphic connections: the sl_2 case, O. Marchal, M. Alameddine, NonLinearity, [arXiv:2306.07378], 2024.
  5. Hamiltonian representation of isomonodromic deformations of twisted rational connections: The Painlevé 1 hierarchy, O. Marchal, M. Alameddine, [arXiv:2302.13905], 2023.
  6. Hamiltonian representation of isomonodromic deformations of general rational connections on gl_2, O. Marchal, N. Orantin, M. Alameddine [arXiv:2212.04833], 2022.
  7. Quantization of classical spectral curves via topological recursion, B. Eynard, E. Garcia-Failde, O. Marchal, N. Orantin, Communications in Mathematical Physics, [arXiv:2106.04339], 2024.
  8. Asymptotic expansion of Toeplitz determinants of an indicator function with discrete rotational symmetry and powers of random unitary matrices, O. Marchal, Letters in Mathematical Physics, [arXiv:2112.01306], 2023.
  9. On the Hurwitz zeta function with an application to the exponential-beta distribution, J. Arbel, O. Marchal, B. Nipoti, Journal of Inequalities and Applications, [arXiv:1909.07026], 2020.
  10. On strict sub-Gaussianity, optimal proxy variance and symmetry for bounded random variables, J. Arbel, O. Marchal, H.D. Nguyen, ESAIM: Probability and Statistics, [arXiv:1901.09188], 2020.
  11. Isomonodromic deformations of a rational differential system and reconstruction with the topological recursion: the sl_2 case, O. Marchal, N. Orantin, Journal of Mathematical Physics, [arXiv:1901.04344], 2020.
  12. Quantization of hyper-elliptic curves from isomonodromic systems and topological recursion, O. Marchal, N. Orantin, Journal of Geometry and Physics , [arXiv:1911.07739], 2019.
  13. Asymptotic expansions of some Toeplitz determinants via the topological recursion, O. Marchal, Letters in Mathematical Physics, [arXiv:1611.05627], 2019.
  14. Painlevé equations, topological type property and reconstruction by the topological recursion, K. Iwaki, O. Marchal, A. Saenz, Journal of Geometry and Physics, [arXiv:1601.02517], 2018.
  15. Application de la récurrence topologique aux intégrales et matrices aléatoires et aux systèmes intégrables, O. Marchal, Habilitation à diriger des recherches, [arXiv:1710.06705], 2017.
  16. On the sub-Gaussianity of the Beta and Dirichlet distributions, O. Marchal, J. Arbel, Electronic Communications in Probability, [arXiv:1705.00048], 2017.
  17. WKB solutions of difference equations and reconstruction by the topological recursion, O. Marchal, Nonlinearity, [arXiv:1703.06152], 2017.
  18. Integrable differential systems of topological type and reconstruction by the topological recursion, B. Eynard, O. Marchal, R. Belliard, Annales Institut Henri Poincaré, [arXiv:1610.00496], 2017.
  19. Loop equations from differential systems on curves, B. Eynard, O. Marchal, R. Belliard, Annales Institut Henri Poincaré, [arXiv:1602.01715], 2017.
  20. Matrix models, Toeplitz determinants and recurrence times for powers of random unitary matrices, O. Marchal, Random Matrices: Theory and applications, [arXiv:1412.3085], 2014.
  21. Painlevé 2 equation with arbitrary monodromy parameter, topological recursion and determinantal formulas, K. Iwaki, O. Marchal, Annales Institut Henri Poincaré, [arXiv:1411.0875], 2017.
  22. Elements of proof for conjectures of Witte and Forrester about the combinatorial structure of Gaussian Beta Ensembles, O. Marchal, Journal of High Energy Physics, [arXiv:1405.1182], 2014.
  23. The sine-law gap probability, Painlevé 5, and asymptotic expansion by the topological recursion, O. Marchal, B. Eynard, M. Bergère, Random Matrices: Theory and Applications, [arXiv:1311.3217], 2014.
  24. The remodeling conjecture and the Faber-Pandharipande formula, V. Bouchard, A. Catuneanu, O. Marchal, P. Sulkowski, Letters in Mathematical Physics, [arXiv:1108.2689], 2013.
  25. Loop equations and topological recursion for the arbitrary β-two-matrix model, M. Bergère, B. Eynard, O. Marchal, A. Prats-Ferrer, Journal of High Energy Physics, [arXiv:1106.0332], 2012.
  26. One cut solution of the β-ensembles in the Zhukovsky variable, O. Marchal, Journal of Statistical Mechanics, [arXiv:1105.0453], 2012.
  27. Aspects géométriques et intégrables des modèles de matrices aléatoires, O. Marchal, Ph.D. manuscript, [arXiv:1012.4513], 2010.
  28. Topological expansion of β-ensemble model and quantum algebraic geometry in the sector-wise approach, L.O. Chekhov, B. Eynard, O. Marchal, Theoretical and Mathematical Physics, [arXiv:1009.6007], 2010.
  29. A matrix model for the topological string II: The spectral curve and the mirror geometry, B. Eynard, A. Kashani-Poor, O. Marchal, Annales Institut Henri Poincaré, [arXiv:1007.2194], 2010.
  30. A matrix model for the topological string I: Deriving the matrix model, B. Eynard, A. Kashani-Poor, O. Marchal, Annales Institut Henri Poincaré, [arXiv:1003.1737], 2010.
  31. Double scaling limits of random matrices and minimal (2m,1) models: the merging of two cuts in a degenerate case, O. Marchal, M. Cafasso, Journal of Statistical Mechanics, [arXiv:1002.3347], 2010.
  32. Topological expansion of the Bethe ansatz and quantum algebraic geometry, L.O. Chekhov, B. Eynard, O. Marchal, [arXiv:0911.1664], 2009.
  33. Topological expansion of the Bethe ansatz and non-commutative algebraic geometry, B. Eynard, O. Marchal, Journal of High Energy Physics, [arXiv:0809.3367], 2009.
  34. The partition function of the two-matrix models as an isomonodromic tau-function, M. Bertola, O. Marchal, Journal of Mathematical Physics, [arXiv:0809.1598], 2009.

Publications associated with data analysis:

  1. Evolution and Predictive Factors of Improvement of Obstructive Sleep Apnea in an Obese Population After Bariatric Surgery, F. Magne, E. Gomez, O. Marchal, P. Malvestio, N. Riebel, L. Brunaud, O. Ziegler, D. Quilliot, F. Chabot, A. Chaouat, Journal of clinical sleep medicine, 2019.
  2. 420 Report of 97 transitioning adolescents with cystic fibrosis from paediatric to adult care CF center, F. Magne, S. Durupt, R. Nove-Josserand, M. Perceval, O. Marchal, P. Reix, I. Durieu, Q. Reynaud, Journal of Cystic Fibrosis, 2017.
  3. Évolution et facteurs prédictifs d'amélioration du SAHOS après chirurgie bariatrique par court-circuit gastrique dans une population d'obèses grades 2 et 3, F. Magne, E. Gomez, O. Marchal, P. Malvestio, N. Riebel, L. Brunaud, O. Ziegler, D. Quilliot, F. Chabot, A. Chaouat, Revue des Maladies Respiratoires, 2017.
  4. Dermoscopy: A useful tool for general practitioners in melanoma screening: A nationwide survey, P. Chappuis, G. Duru, O. Marchal, P. Girier, S. Dalle, L. Thomas, British Journal of Dermatology, 2016.

PhD. students

  1. Mohamad Alameddine, since Sept. 2022