Abstract
Let Ω be a region in the plane which contains the origin, is star-shaped with respect to the origin and has a piecewise C1 boundary. For each integer Q ≥ 1, we consider the integer lattice points from ΩQ = {(Qx, Qy); (x, y) ∈ Ω} which are visible from the origin and prove that the 1st consecutive spacing distribution of the angles formed with the origin exists. This is a probability measure supported on an interval [mΩ, ∞), with mΩ > 0. Its repartition function is explicitly expressed as the convolution between the square of the distance from origin function and a certain kernel.
Original language | English (US) |
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Pages (from-to) | 433-470 |
Number of pages | 38 |
Journal | Communications in Mathematical Physics |
Volume | 213 |
Issue number | 2 |
DOIs | |
State | Published - Sep 2000 |
Externally published | Yes |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics