Publications

1. Central Limit Theorem for tensor products of free variables

Cécilia Lancien, Patrick Oliveira Santos, Pierre Youssef

Canadian Journal of Mathematics, 2024 (arxiv here)

2. Limiting Spectral Distribution of Random Self-Adjoint Quantum Channels

Cécilia Lancien, Patrick Oliveira Santos, Pierre Youssef

Mathematical Physics, Analysis and Geometry, 2024 (arxiv here)

3. Almost Sharp Bounds for Heteroskedastic Wishart Random Matrices

Patrick Oliveira Santos

Accepted in Pafa, 2025 (arxiv here)

Preprints

1. Khintchine inequalities, trace monoids and Turán type problems

Patrick Oliveira Santos, Raghavendra Tripathi, Pierre Youssef

Arxiv here

2. Central limit theorems for ϵ-Independent products and higher-order tensors

Guillaume Cébron, Patrick Oliveira Santos, Pierre Youssef

Arxiv here

3. Graphon-Theoretic Approach to Central Limit Theorems for ϵ-Independence

Guillaume Cébron, Patrick Oliveira Santos, Pierre Youssef

Arxiv here

4. On spectral outliers of inhomogeneous symmetric random matrices

Dylan J. Altschuler, Patrick Oliveira Santos, Konstantin Tikhomirov, Pierre Youssef

Arxiv here

5. A combinatorial view on star moments of regular directed graphs and trees

Benjamin Dadoun, Patrick Oliveira Santos

Arxiv here

Defenses

• On the moment method for inhomogeneous matrices: from regular graphs to quantum channels

Ph.D. defense, Gustave Eiffel University, 27 Jun 2024 (manuscript here)

• On random matrices: asymptotic and non-asymptotic estimations

Masters defense, Gustave Eiffel University, 13 Set 2021

• On log-Sobolev inequalities and their applications

Masters defense, Federal University of Rio de Janeiro, 16 Jul 2020