In their preface, the authors state that 'this is a book for absolute beginners'. Well, that
depends on the definition of a beginner! Here,(s) he should be thoroughly at home in …

arXiv:2407.21194v1 [math-ph] 30 Jul 2024 Page 1 Lectures on Coulomb and Riesz Gases
Sylvia Serfaty arXiv:2407.21194v1 [math-ph] 30 Jul 2024 Page 2 Page 3 Contents Preface 5 …

We study the fluctuations of the largest eigenvalue λ max of N× N random matrices in the
limit of large N. The main focus is on Gaussian β ensembles, including in particular the …

Covariances and variances of linear statistics of a point process can be written as integrals
over the truncated two-point correlation function. When the point process consists of the …

We study a system of N noninteracting spinless fermions trapped in a confining potential, in
arbitrary dimensions d and arbitrary temperature T. The presence of the confining trap …

The Toda chain is the prime example of a classical integrable system with strictly local
conservation laws. Relying on the Dumitriu–Edelman matrix model, we obtain the …

Unlike the well-known Mott's argument that extended and localized states should not coexist
at the same energy in a generic random potential, we formulate the main principles and …

We study N vicious Brownian bridges propagating from an initial configuration {a 1< a 2<…<
a N} at time t= 0 to a final configuration {b 1< b 2<…< b N} at time t= tf, while staying non …

We report on molecular dynamics simulations of spacetime correlations of the Toda lattice in
thermal equilibrium. The correlations of stretch, momentum, and energy are computed …

Duality identities in random matrix theory for products and powers of characteristic
polynomials, and for moments, are reviewed. The structure of a typical duality identity for the …