8 problems

The Boltzmann–Grad limit of the Lorentz gas describes the dynamics of a tagged particle as the radius of the fixed scatterers tends to zero. Lorentz's conjecture. The limiting syst…

Let $\gamma<-1$, and let $W(\lambda)$ denote the weight appearing in the spectral representation of the macroscopic quantity $\rho_g$. Write $n$ for the parameter satisfying the re…

The Lorentz gas is the billiard system in ${\mathbb R}^d$ with $d\geq 2$ and identical, fixed spherical scatterers in an otherwise arbitrary configuration satisfying the stated gen…

Consider the process $\mathbb P_\star$ of admissible jumps in the random environment $\Omega$, induced by the deterministic billiard dynamics. A process is said to be a random walk…

Correlation-decay conjecture. For $d\geq 3$, correlations restricted to trajectories with at least one collision should decay more rapidly than $C/t$; subject to this conjecture,

Consider the two-dimensional quasiperiodic Lorentz gas obtained by projecting a three-dimensional simple cubic lattice with cubic unit cell $C$ onto a totally irrational plane $E$…

Let $F(t)$ be the free flight survival probability for a $d$-dimensional periodic Lorentz gas with an incipient, but no actual, principal horizon. Incipient-horizon decay conjectur…

A Lorentz gas consists of strictly convex obstacles of class $C^3$; it satisfies the finite horizon condition when the minimal distance between obstacles is strictly positive and e…