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math.PR2025
On the Rigidity of Projected Perturbed Lattices
Youssef Djellouli, Pierre Yves Gaudreau Lamarre
We study the occurrence of number rigidity and deletion singularity in a class of point processes that we call {\it projected perturbed lattices}. These are generalizations of proc…
math.PR2025
On the Spectral Geometry and Small Time Mass of Anderson Models on Planar Domains
Pierre Yves Gaudreau Lamarre, Yuanyuan Pan
We consider the Anderson Hamiltonian (AH) and the parabolic Anderson model (PAM) with white noise and Dirichlet boundary condition on a bounded planar domain .…
math.PR2025
Recovering Parameters from Edge Fluctuations: Beta-Ensembles and Critically-Spiked Models
Pierre Yves Gaudreau Lamarre
Let be the point process that describes the edge scaling limit of either (i) "regular" beta-ensembles with inverse temperature , or (ii) the top eig…