P. Lamarre

activity

20162026

most cited

*

-Freeness in Finite Tensor Products

5 citations · 10 across the 14 of their papers we have counts for

collaborators

Showing math.PRShow all

14 papers · 1 filter

math.PR2026

The Parabolic Anderson Model's Total Mass at Small Times: Geometry, Fluctuations, and Renormalization

Pierre Yves Gaudreau Lamarre, Yuanyuan Pan

Let $D \subset R^{d}$ be a bounded domain, let $κ > 0$ be fixed, and let $W$ be a fractional Brownian sheet on $R \times R^{d}$ . Consider the Stratonovich parabolic A…

math.PR2026

Optimal Covariance Estimates for Schrödinger Semigroups with White Noise in $d = 1, 2$

Youssef Djellouli, Pierre Yves Gaudreau Lamarre

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

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 $D \subset R^{2}$ .…

math.PR2025

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

Pierre Yves Gaudreau Lamarre

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

math.PR2024

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

Pierre Yves Gaudreau Lamarre

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

math.PR2023

Probabilistic Representations of Ordered Exponentials: Vector-Valued Schrödinger 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…

math.PR2022★ 1 cited

Moment Intermittency in the PAM with Asymptotically Singular Noise

Pierre Yves Gaudreau Lamarre, Promit Ghosal, Yuchen Liao

Let $ξ$ be a singular Gaussian noise on $R^{d}$ that is either white, fractional, or with the Riesz covariance kernel; in particular, there exists a scaling parameter $ω > 0$ s…

math.PR2021

Rigidity of the Stochastic Airy Operator

Pierre Yves Gaudreau Lamarre, Promit Ghosal, Wenxuan Li +1

We prove that the spectrum of the stochastic Airy operator is rigid in the sense of Ghosh and Peres (Duke Math. J., 166(10):1789--1858, 2017) for Dirichlet and Robin boundary condi…

math.PR2020★ 2 cited

Phase Transitions in Asymptotically Singular Anderson Hamiltonian and Parabolic Model

Pierre Yves Gaudreau Lamarre

Let $ξ$ be a Gaussian white noise on $R^{d}$ ( $d = 1, 2, 3$ ). Let $(ξ_{ε})_{ε > 0}$ be continuous Gaussian processes such that $ξ_{ε} \to ξ$ as $\varepsilon…

math.PR2019

Asymptotic Freeness of Unitary Matrices in Tensor Product Spaces for Invariant States

Benoît Collins, Pierre Yves Gaudreau Lamarre, Camille Male

In this paper, we pursue our study of asymptotic properties of families of random matrices that have a tensor structure. In previous work, the first- and second-named authors provi…

math.PR2019

On the Convergence of Random Tridiagonal Matrices to Stochastic Semigroups

Pierre Yves Gaudreau Lamarre

We develop an improved version of the stochastic semigroup approach to study the edge of $β$ -ensembles pioneered by Gorin and Shkolnikov, and later extended to rank-one additive pe…

math.PR2018★ 2 cited

Joint and Conditional Local Limit Theorems for Lattice Random Walks and Their Occupation Measures

Pierre Yves Gaudreau Lamarre

Let $S_{n}$ be a lattice random walk with mean zero and finite variance, and let $Λ_{n}^{a}$ be its occupation measure at level $a$ . In this note, we prove local limit theorems for $\Pr[…

math.PR2017

Edge of spiked beta ensembles, stochastic Airy semigroups and reflected Brownian motions

Pierre Yves Gaudreau Lamarre, Mykhaylo Shkolnikov

We access the edge of Gaussian beta ensembles with one spike by analyzing high powers of the associated tridiagonal matrix models. In the classical cases beta=1, 2, 4, this corresp…

The Parabolic Anderson Model's Total Mass at Small Times: Geometry, Fluctuations, and Renormalization

Optimal Covariance Estimates for Schrödinger Semigroups with White Noise in d=1,2

On the Rigidity of Projected Perturbed Lattices

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

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

Probabilistic Representations of Ordered Exponentials: Vector-Valued Schrödinger Semigroups and the Combinatorics of Anderson Localization

Moment Intermittency in the PAM with Asymptotically Singular Noise

Rigidity of the Stochastic Airy Operator

Phase Transitions in Asymptotically Singular Anderson Hamiltonian and Parabolic Model

Asymptotic Freeness of Unitary Matrices in Tensor Product Spaces for Invariant States

On the Convergence of Random Tridiagonal Matrices to Stochastic Semigroups

Joint and Conditional Local Limit Theorems for Lattice Random Walks and Their Occupation Measures

Edge of spiked beta ensembles, stochastic Airy semigroups and reflected Brownian motions

Optimal Covariance Estimates for Schrödinger Semigroups with White Noise in $d = 1, 2$