Higher-order transport commutators and cumulants of linear statistics — A brief note explaining how higher-order transport-commutator expressions arise naturally when computing cumulants of linear statistics of a Gibbs ensemble. It is stated for Coulomb/Riesz gas ensembles, but the argument is not specific to the interaction.
Uniform LSI for the subcritical Kuramoto model — A short note explaining how work of Bauerschmidt and Bodineau on uniform logarithmic Sobolev inequalities for spin systems implies a uniform LSI for the Kuramoto model (the \(O(2)\), or classical XY, model) above the critical temperature.
Uniform-in-time mean-field convergence for 2D Coulomb gradient flows — Exponentially fast relaxation to the uniform distribution and uniform-in-time mean-field convergence for any \(L^\infty\) probability density.
Beyond Gronwall for gradient flows — A short note on noiseless mean-field convergence with a polynomial, rather than exponential, time factor in some Coulomb gradient flows.
Pickl’s method for \(H^1\) data — A note using dispersion of the limiting equation to reduce the regularity assumptions in Pickl’s derivation of the three-dimensional Gross–Pitaevskii equation.
Convolution inequalities for the Boltzmann collision operator — Notes based on work of Alonso, Carneiro, and Gamba.
Critical conditional global well-posedness and scattering for cubic NLS in \(\mathbb{R}^3\) — Notes based on work of Kenig and Merle.
Introduction to Fourier analysis on the torus — An introduction to Fourier analysis on \(\mathbb{T}^d\), including Kolmogorov’s construction of an \(L^1(\mathbb{T})\) function whose Dirichlet means diverge pointwise almost everywhere.