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The periodic Lorentz gas describes the dynamics of a point particle in a periodic array of spherical scatterers, and is one of the fundamental models for chaotic diffusion. In the present paper we… (More)

- Jens Marklof
- 1999

For almost all values of x 2 R, the classical theta sum S N (x) = N ?1=2 N X n=1 e 2i n 2 x exhibits an extremely irregular behaviour, as N tends to innnity. This limit is investigated by exploiting… (More)

We study the dynamics of a point particle in a periodic array of spherical scatterers and construct a stochastic process that governs the time evolution for random initial data in the limit of low… (More)

- Jens Marklof
- 2010

The Frobenius number F(a) of an integer vector a with positive coprime coefficients is defined as the largest number that does not have a representation as a positive integer linear combination of… (More)

- Jens Marklof
- 2004

- Jens Marklof, Andreas Strömbergsson
- Combinatorica
- 2011

The diameter of a graph measures the maximal distance between any pair of vertices. The diameters of many small-world networks, as well as a variety of other random graph models, grow logarithmically… (More)

The periodic Lorentz gas describes an ensemble of non-interacting point particles in a periodic array of spherical scatterers. We have recently shown that, in the limit of small scatterer density… (More)

Previous studies of kinetic transport in the Lorentz gas have been limited to cases where the scatterers are distributed at random (e.g., at the points of a spatial Poisson process) or at the… (More)

The dynamics of a point particle in a periodic array of spherical scatterers converges, in the limit of small scatterer size, to a random flight process, whose paths are piecewise linear curves… (More)

AbstractIt is well known that (i) for every irrational number α the Kronecker
sequence mα (m = 1,...,M) is equidistributed modulo one in the
limit
$$ \rightarrow\infty $$
, and (ii) closed… (More)