Recherche - Research

Tous les noms d'articles pointent vers la version arXiv, sauf pour les articles publiés en open access, où ils amènent vers la version publiée.

All article names point to the arXiv version, except for articles published in open access, where they point to the published version.

Publications et prépublications - Publication and preprints

1. Number variance for homogeneous determinantal point processes in hyperbolic spaces. Preprint, 2025.

In the cas of homogeneous determinantal point process on a Gromov hyperbolic metric space, we give a lower bound of the variance of the number of points inside a ball that is proportional to the volume of that ball.

2.  The 2D Toda lattice hierarchy for multiplicative functionals of Schur measures. Preprint, 2024.

Using the formalism of the fermionic Fock space and the Boson-Fermion correspondance, we prove that multiplicative functionals of Schur measures, as well as gap probability of finite temperature Schur measures, are tau functions of the 2D Toda lattice hierarchy. 

3. Explicit description of Christoffel deformations and Palm measures of the Plancherel measure, the z-measures and the Gamma process. , Bull. Sci. math. (2025), https://doi.org/10.1016/j.bulsci.2025.103693 (in press)

From the descritption of Christoffel deformations of orthogonal polynomial ensembles, we derive explicit formulas for the correlation kernels of Palm measures and Christoffel deformations of the Plancherel measure, the z-measures and the Gamma process, involving determinants in the relevant special functions.

4. Accumulated spectrograms for hyperuniform determinantal point processes. Avec Makoto Katori et Tomoyuki Shirai. Preprint, 2024. To appear in Journal of Mathematical Physics.

We prove a convergence Theorem for accumulated spectrograms associated to a locally trace class orthogonal projection giving rise to a hyperuniform determinantal point process along an exhaustion. We prove that any radial determinantal point process governed by an orthogonal projection is hyperuniform along the dilation of an open bounded set, and that the accumulated spectrogram converges to the indicator function of that set.

5. A law of large numbers for local patterns in Schur measures and a Schur process. Journal of Theoretical Probability, Vol. 38, No 55 (2025).

For a class of Schur measures and for a model of random plane partitions, we prove that the properly scaled linear statistics of a function, weighted by the appearance of a given pattern converges to the integral of that function on the limit shape, weighted by the probability of appearance of the pattern for the local limit point processes.

6. A determinantal point process governed by an integrable projection kernel is Giambelli compatible. Avec Alexander I. Bufetov. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XXVI (2025), 525-559. https://arxiv.org/abs/2111.05606

For a determinantal point process on the real line governed by an integrable projection kernel, we prove that the expectation of a product of ratio of characteristic     polynomials is expressed as a determinant in the expectations of the ratios. This formula is equivalent to the stability of the Giambelli formula for Schur functions under averaging.

7. The Hyperbolic-type Point Process. Avec Nizar Demni. J. Math. Soc. Japan 71(4): 1137-1152 (2019). 

We introduce a two-parameter family of determinantal point processes in the Poincaré disk associated to the Landau levels of the magnetic Laplacian. Our main result is an explicit computation of the variance of the number of points inside a large ball.