Planning

Monday, March 25, 2024

Time Event  
09:00 - 09:30 Welcome - Welcome  

Tuesday, March 26, 2024

Time Event  
09:00 - 09:30 Welcome - Welcome  
09:30 - 10:45 Class - Laure Dumaz's mini-class  
10:45 - 11:00 Coffee break  
11:00 - 12:15 Class - Thomas Leblé's mini-class  
12:15 - 14:00 Lunch  
14:00 - 14:30 Talk Branching random walk - Joelle Ishak's talk 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.  
14:30 - 15:00 Talk Statistics of local level spacings in quantum chaology - Peng Tian's talk: 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.  
15:00 - 15:15 Break  
15:15 - 15:55 Talk Topological expansion of unitary integrals and maps - Exposé de Thomas Buc d'Alché 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.  
15:55 - 16:10 Break  
16:10 - 16:40 Talk Universality for least singular value of alpha-stable RM - Michalis Louvaris's talk 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.  

Wednesday, March 27, 2024

Time Event  
09:30 - 10:45 Class - Thomas Leblé's mini-class  
10:45 - 11:00 Coffee break  
11:00 - 12:15 Class - Laure Dumaz's mini-class  
12:15 - 14:00 Lunch  
14:00 - 18:00 Hike - Hike  

Thursday, March 28, 2024

Time Event  
09:30 - 10:45 Class - Laure Dumaz's mini-class  
10:45 - 11:00 Coffee break  
11:00 - 12:15 Class - Thomas Leblé's mini-class  
12:15 - 14:00 Lunch  
14:00 - 14:40 Talk Asymptotics in beta ensembles at high temperature - Charlie Dworaczek Guera's talk 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.  
14:40 - 15:00 Talk Random Matrix Approach to Tensor Approximation - Hugo Lebeau's talk. 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.  
15:00 - 15:15 Break  
15:15 - 15:35 Talk De l’écologie aux matrices aléatoires - Mohammed-Younes GUEDDARI's talk 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.  
15:35 - 15:55 Talk Chemical potential from correlation functions. - Fabio Frommer's talk 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  
15:55 - 16:10 Break  
16:10 - 16:30 Talk Gaussian fluctuation for the Elliptic Ginibre Ensemble - Talk of 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.  
16:30 - 16:50 Talk correlation functions in Sinh-Gordon 1+1 QFT - Alex Simon's talk: Abstract: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.  

Friday, March 29, 2024

Time Event  
09:30 - 10:00 Talk Monte Carlo with Gibbs measures - Martin Rouault's talk  
10:00 - 10:15 Coffee break  
10:15 - 10:45 Talk DLR equations for the Bose gas - -  
11:15 - 12:30 Grabing food and departure - TBA  
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