Programme
| Heures |
événement |
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09:00 - 09:30
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Accueil - Accueil |
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| Heures |
événement |
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09:00 - 09:30
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Accueil - Accueil |
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09:30 - 10:45
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Cours - Mini-cours de Laure Dumaz |
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10:45 - 11:00
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Pause café |
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11:00 - 12:15
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Cours - Mini-cours de Thomas Leblé |
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12:15 - 14:00
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Déjeuner |
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14:00 - 14:30
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Exposé Branching random walk - Exposé de Joelle Ishak
Abstract:
Branching random walk is a stochastic process that combines the concepts of branching processes and random
walks, offering a powerful framework to study a wide range of phenomena, including population dynamics,
particle systems, and epidemic spreading. |
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14:30 - 15:00
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Exposé Statistics of local level spacings in quantum chaology - Exposé de Peng Tian:
Abstract: We introduce a notion of local level spacings and study their statistics within a random-matrix-theory approach. In the limit of infinite-dimensional random matrices, we determine universal sequences of mean local spacings and of their ratios which uniquely identify the global symmetries of a quantum system and its internal -- chaotic or regular -- dynamics. These findings, which offer a new framework to monitor single- and many-body quantum systems, are corroborated by numerical experiments performed for zeros of the Riemann zeta function, spectra of irrational rectangular billiards and many-body spectra of the Sachdev-Ye-Kitaev (SYK) Hamiltonians. |
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15:00 - 15:15
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Pause |
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15:15 - 15:55
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Exposé Topological expansion of unitary integrals and maps - Thomas Buc d'Alché's talk
Abstract: Consider integrals on the unitary group, with respect to the Haar measure. The asympotic expansion of such integrals when the dimension tends to infinity can be expressed in terms of maps, i.e. graphs embedded in surfaces. These particular maps generalize the monotone Hurwitz numbers. |
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15:55 - 16:10
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Pause |
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16:10 - 16:40
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Exposé Universality for least singular value of alpha-stable RM - Exposé de Michalis Louvaris
Abstract
This talk investigates the asymptotic behavior of the least singular value a heavy-tailed random matrix model, random matrices with alpha-stable entries. We establish that the asymptotic distribution is the same as in the models with finite variance, for example when the entries of the matrix are Gaussian random variables, as the dimension of the matrices grows to infinity.
The methods used to establish the result are based on the three step strategy, an important strategy developed in the last decade in the random matrix theory literature. |
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| Heures |
événement |
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09:30 - 10:45
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Cours - Mini-cours de Thomas Leblé |
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10:45 - 11:00
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Pause café |
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11:00 - 12:15
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Cours - Mini-cours de Laure Dumaz |
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12:15 - 14:00
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Déjeuner |
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14:00 - 18:00
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Randonnée - Randonnée |
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| Heures |
événement |
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09:30 - 10:45
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Cours - Mini-cours de Laure Dumaz |
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10:45 - 11:00
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Pause café |
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11:00 - 12:15
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Cours - Mini-cours de Thomas Leblé |
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12:15 - 14:00
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Déjeuner |
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14:00 - 14:40
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Exposé Asymptotics in beta ensembles at high temperature - Exposé de Charlie Dworaczek Guera
Abstract: In the celebrated beta-ensemble model, one can choose to pick the temperature proportional to the number of particles. In this regime, entropy plays a role in the determination of the equilibrium measure. We show CLT and asymptotics of the partition function. |
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14:40 - 15:00
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Exposé Random Matrix Approach to Tensor Approximation - Exposé de Hugo Lebeau
Abstract:
This work presents a comprehensive understanding of the estimation of a planted low-rank signal from a general spiked tensor model near the computational threshold. Relying on standard tools from the theory of large random matrices, we characterize the large-dimensional spectral behavior of the unfoldings of the data tensor and exhibit relevant signal-to-noise ratios governing the detectability of the principal directions of the signal. These results allow to accurately predict the reconstruction performance of truncated multilinear SVD (MLSVD) in the non-trivial regime. This is particularly important since it serves as an initialization of the higher-order orthogonal iteration (HOOI) scheme, whose convergence to the best low-multilinear-rank approximation depends entirely on its initialization. We give a sufficient condition for the convergence of HOOI and show that the number of iterations before convergence tends to $1$ in the large-dimensional limit. |
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15:00 - 15:15
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Pause |
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15:15 - 15:35
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Exposé De l’écologie aux matrices aléatoires - Exposé de Mohammed-Younes GUEDDARI
Abstract:
L’analyse du point d’équilibre dans un système Lotka-Volterra, qui régit les interactions complexes entre espèces, constitue un défi inhérent à la modélisation écologique. Notre recherche, se démarquant par son contexte de grande dimension, aborde cette problématique en utilisant un modèle de matrice d’interaction aléatoire de grande dimension [May72]. On établit également une connexion intrigante avec le Linear Complementarity Problem (LCP) [AHMN23] qui est un problème d’optimisation classique. Nous utilisons les algorithmes Approximate Message Passing (AMP) [FVRS21], reconnus comme des outils analytiques très puissants, pour étudier les propriétés statistiques du point d’équilibre. Notre travail se concentre sur l’extension de ces algorithmes, tra- ditionnellement appliqués à des matrices symétriques, afin de les adapter à des matrices non symétriques. Nous examinons plus particulièrement les matrices d’interaction ellip- tiques pour une modélisation plus réaliste des interactions complexes et asymétriques entre espèces au sein des écosystèmes. Si le temps le permet, je présenterai également des résultats de la propagation du chaos [Szn91]. En les appliquant à notre problème d’écologie théorique, ces résultats fourniront des insights plus fins sur les propriétés statistiques des sous-populations partageant des propriétés de croissance intrinsèques similaires. |
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15:35 - 15:55
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Exposé Chemical potential from correlation functions. - Exposé de Fabio Frommer
Abstract:
Interacting particle systems in a finite volume in equilibrium are often described by a grand canonical ensemble induced by the corresponding Hamiltonian, i.e. a finite volume Gibbs measure. However, in practice, directly measuring this Hamiltonian is not possible, as such, methods need to be developed to calculate the Hamiltonian potentials from measurable data. In this work we give an expansion of the chemical potential in terms of the correlation functions of such a system in the thermodynamic limit. This is a justification of a formal approach of Nettleton and Green from the 50's |
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15:55 - 16:10
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Pause |
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16:10 - 16:30
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Exposé Gaussian fluctuation for the Elliptic Ginibre Ensemble - Exposé Sylvain Chabredier
Abstract. The elliptic Ginibre ensemble and the ground state of a free Fermi gas associated with a quadratic potential are two linked determinantal point processes for which the kernel is known exactly. In this talk, I will show recent results that we obtained jointly with Gaultier Lambert, describing the gaussian fluctuations of these point processes.
For the Elliptic Ginibre Ensemble, I will present a uniform central limit theorem valid for linear statistics of the points (uniform for the correlation parameter).
For the free Fermi gas, I will present the covariance structure associated with the gaussian fluctuations. |
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16:30 - 16:50
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Exposé correlation functions in Sinh-Gordon 1+1 QFT - Exposé de Alex Simon
Résumé:The 1+1d Sinh-Gordon model is one of the simplest integrable models, but one has yet to construct it as a proper quantum field theory. One way to do it is to study its correlation functions and to make sure these functions are well-defined as series of N-uple integrals. They also have to satisfy several conditions, which are the axioms of Wightman. Here, we establish the well-definition of some truncated multi-point correlation functions and their properties. |
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| Heures |
événement |
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09:30 - 10:00
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Exposé Monte Carlo with Gibbs measures - Exposé de Martin Rouault |
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10:00 - 10:15
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Pause café |
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10:15 - 10:45
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Exposé DLR equations for the Bose gas - - |
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11:15 - 12:30
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Récupération des piques-niques et départ - TBA |
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