Distribution of angles to lattice points seen from a fast moving observer

TL;DR

This paper investigates how the angles to lattice points within an expanding square are distributed from a moving observer, establishing the existence of a limiting gap distribution and deriving explicit density formulas.

Contribution

It introduces a novel analysis of angle distributions from a non-uniformly moving observer towards expanding lattice points, with explicit formulas for the limiting distribution.

Findings

Existence of a gap distribution as time approaches infinity

Explicit formulas derived for the density function of the distribution

Analysis of angles from a uniformly expanding square observed from an accelerating observer

Abstract

We consider a square expanding with constant speed seen from an observer moving away with constant acceleration and study the distribution of angles between rays from the observer towards the lattice points in the square. We prove the existence of the gap distribution as time tends to infinity and provide explicit formulas for the corresponding density function.