P. Lamarre

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20242026

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math.PR2026

Optimal Covariance Estimates for SchrÃ¶dinger Semigroups with White Noise in $d = 1, 2$

Youssef Djellouli, Pierre Yves Gaudreau Lamarre

For $d \in {1, 2}$ , let $H = - \frac{1}{2} I^ + V + I^¾$ be the random SchrÃ¶dinger operator on $L^{2} (R^{d})$ where $I^¾$ is a standard Gaussian white noise and $V$ is a deterministic…

math.PR2026

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 $D \subset R^{2}$ .…

math.PR2025

Recovering Parameters from Edge Fluctuations: Beta-Ensembles and Critically-Spiked Models

Pierre Yves Gaudreau Lamarre

Let $I^ = {I^_{0}, I^_{1}, I^_{2}, \dots}$ be the point process that describes the edge scaling limit of either (i) "regular" beta-ensembles with inverse temperature $I^^{2} > 0$ , or (ii) the to…

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

Trace Moments for SchrÃ¶dinger Operators with Matrix White Noise and the Rigidity of the Multivariate Stochastic Airy Operator

Pierre Yves Gaudreau Lamarre

We study the semigroups of random SchrÃ¶dinger operators of the form $H f = - \frac{1}{2} f^{''} + (V + I^¾) f$ , where $f : I \to F^{r}$ ( $F = R, C, H$ ) are v…

math.PR2024

Probabilistic Representations of Ordered Exponentials: Vector-Valued SchrÃ¶dinger Semigroups and the Combinatorics of Anderson Localization

Pierre Yves Gaudreau Lamarre

We provide two applications of an elementary (yet seemingly unknown) probabilistic representation of matrix ordered exponentials, which generalizes the Feynman-Kac formula in finit…

Optimal Covariance Estimates for SchrÃ¶dinger Semigroups with White Noise in d=1,2

On the Spectral Geometry and Small Time Mass of Anderson Models on Planar Domains

Recovering Parameters from Edge Fluctuations: Beta-Ensembles and Critically-Spiked Models

On the Rigidity of Projected Perturbed Lattices

Trace Moments for SchrÃ¶dinger Operators with Matrix White Noise and the Rigidity of the Multivariate Stochastic Airy Operator

Probabilistic Representations of Ordered Exponentials: Vector-Valued SchrÃ¶dinger Semigroups and the Combinatorics of Anderson Localization

Optimal Covariance Estimates for SchrÃ¶dinger Semigroups with White Noise in $d = 1, 2$