Pierre Yves Gaudreau Lamarre

Pierre Yves Gaudreau Lamarre

I am an Assistant Professor in the Department of Mathematics at Syracuse University.
Previously, I was a William H Kruskal Instructor at the University of Chicago. I completed a PhD at Princeton University with Mykhaylo Shkolnikov, and a BSc & MSc at the University of Ottawa with Benoît Collins.

I can be contacted at pgaudrea at syr.edu.

My research focus lies in probability, functional analysis, and mathematical physics. In the past years, I have worked on problems involving random Schrödinger operators and semigroups, stochastic partial differential equations, large random matrices, and free probability.

Preprints & Publications

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

Preprint

Exact Multi-Point Correlations in the Stochastic Heat Equation for Strictly Sublinear Coordinates

with Yier LinPreprint

Moment Intermittency in the PAM with Asymptotically Singular Noise [arXiv]

with Promit Ghosal and Yuchen LiaoTransactions of the American Mathematical Society

Rigidity of the Stochastic Airy Operator [arXiv]

with Promit Ghosal, Wilson Li, and Yuchen LiaoInternational Mathematics Research Notices

KPZ Equation with a Small Noise, Deep Upper Tail and Limit Shape [arXiv]

with Li-Cheng Tsai and Yier LinProbability Theory and Related Fields

On Spatial Conditioning of the Spectrum of Discrete Random Schrödinger Operators [arXiv]

with Promit Ghosal and Yuchen LiaoJournal of Spectral Theory

Phase Transitions in Asymptotically Singular Anderson Hamiltonian and Parabolic Model [arXiv]

Stochastics and Partial Differential Equations

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

with Benoît Collins and Camille MaleRandom Matrices: Theory and Applications

Spectral Rigidity of Random Schrödinger Operators via Feynman-Kac Formulas [arXiv]

with Promit Ghosal and Yuchen LiaoAnnales Henri Poincaré - Theoretical and Mathematical Physics

On the Convergence of Random Tridiagonal Matrices to Stochastic Semigroups [arXiv]

Annales de l’Institut Henri Poincaré - Probabilités et Statistiques

Semigroups for One-Dimensional Schrödinger Operators with Multiplicative Gaussian Noise [arXiv]

Electronic Journal of Probability

Edge of Spiked Beta Ensembles, Stochastic Airy Semigroups and Reflected Brownian Motions [arXiv]

with Mykhaylo ShkolnikovAnnales de l’Institut Henri Poincaré - Probabilités et Statistiques

∗-Freeness in Finite Tensor Products [arXiv]

with Benoît CollinsAdvances in Applied Mathematics

Lecture Notes & Theses

Introduction to Mathematical Probability

Lecture Notes for STAT 25100 at the University of Chicago

Mathematics of Quantum Mechanics

Lecture Notes for MATH 18600 at the University of Chicago

Topics in Random Matrix Theory

Lecture Notes for CAAM/STAT 38520 at the University of Chicago

Semigroups for One-Dimensional Schrödinger Operators with Multiplicative Gaussian Noise

PhD Thesis

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

Unpublished Note

The Theory of Free Probability and Some Applications in the Study of Random Matrices

MSc Thesis

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