2025/11/13 by Youssef Djellouli, Pierre Yves Gaudreau Lamarre, Djellouli, Youssef +1
Materials Science · Mathematics · #FOS: Mathematics #Probability (math.PR) #Quasicrystal Structures and Properties #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2511.10610
openalex publication_date 2025/11/13 · openalex created_date 2025/11/15 · openalex updated_date 2026/07/28
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 processes of the form Π=\‖z‖α+gz\z∈ℤd where (gz)z∈ℤd are jointly Gaussian, α>0, d∈ℕ, and ‖⋅‖ is a norm. We develop a new technique to prove sufficient conditions for the deletion singularity of Π, which improves significantly on the conditions one can obtain using the standard rigidity toolkit (e.g., the variance of linear statistics). In particular, we obtain the first lower bounds on α for the deletion singularity of Π that are independent of the dimension d and the correlation of the gz's.