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math.PR2026
Regularization of a stationary point process by a stationary increments perturbation
Loïc Thomassey, Raphaël Lachièze-Rey, Assaf Shapira
We present a novel procedure where a stationary point process is regularized through the convolution with a continuous random field with stationary increments, in the sense that th…
math.PR2025
Perturbed Palm measures
Loïc Thomassey
We show that the perturbation of a Palm measure by an independent process with stationary increments remains a Palm measure.
math.PR2023
Nodal Replication of Planar Random Waves
Loïc Thomassey, Raphaël Lachièze-Rey
We study the almost periods of the eigenmodes of flat planar manifolds in the high energy limit. We prove in particular that the Gaussian Arithmetic Random Waves replicate almost i…