Distribution of the linear flow length in a honeycomb in the small-scatterer limit.
The structure of higher-dimensional noncommutative tori and metric diophantine approximation.
On certain statistical properties of continued fractions with even and with odd partial quotients
On the distribution of the free path length of the linear flow in a honeycomb
Consider the region obtained by removing from the discs of radius , centered at the points of integer coordinates with . We are interested in the distribution of the free path length (exit time) of a point particle, moving from along a linear trajectory of direction , as . For every integer number , we prove the weak convergence of the probability measures associated with the random variables , explicitly computing the limiting distribution. For , respectively , this result leads...
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