Alessandro Pizzo

On finite rank deformations of Wigner matrices

We study the distribution of the outliers in the spectrum of finite rank deformations of Wigner random matrices under the assumption that the absolute values of the off-diagonal matrix entries have uniformly bounded fifth moment and the abso- lute values of the diagonal entries have uniformly bounded third moment. Using our recent results on the fluctuation of resolvent entries (On fluctuations of matrix entries of regular functions of Wigner matrices with non-identically distributed entries, Unpub- lished manuscript; Fluctuations of matrix entries of regular functions of Wigner matrices, Unpublished manuscript) and ideas from (Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices, Unpublished manuscript), we extend the results by Capitaine, Donati-Martin, and Feral (Ann. Probab. 37 (2009) 1–47; Ann. Inst. Henri Poincare Probab. Stat. 48 (2012) 107–133).

Infraparticle Scattering States in Non-Relativistic QED: I. The Bloch-Nordsieck Paradigm

We construct infraparticle scattering states for Compton scattering in the standard model of non-relativistic QED. In our construction, an infrared cutoff initially introduced to regularize the model is removed completely. We rigorously establish the properties of infraparticle scattering theory predicted in the classic work of Bloch and Nordsieck from the 1930’s, Faddeev and Kulish, and others. Our results represent a basic step towards solving the infrared problem in (non-relativistic) QED.

Infraparticle scattering states in nonrelativistic quantum electrodynamics. II. Mass shell properties

We study the infrared problem in the usual model of quantum electrodynamics with nonrelativistic matter. We prove spectral and regularity properties characterizing the mass shell of an electron and one-electron infraparticle states of this model. Our results are crucial for the construction of infraparticle scattering states, which are treated in a separate paper.

Renormalized Electron Mass in Nonrelativistic QED

Within the framework of nonrelativistic QED, we prove that, for small values of the coupling constant, the energy function,

Quantum Brownian Motion in a Simple Model System

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Absence of Embedded Mass Shells: Cerenkov Radiation and Quantum Friction

, of a dressed electron is twice differentiable in the momentum

Atomism and quantization

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