On Order Types of Random Point Sets

Understand

A simple method to produce a random order type is to take the order type of a random point set.

• We conjecture that many probability distributions on order types defined in this way are heavily concentrated and therefore sample inefficiently the space of order types.
• We present two results on this question.
• First, we study experimentally the bias in the order types of $n$ random points chosen uniformly and independently in a square, for $n$ up to $16$.