---
tag: DNDKBVHS3H
kind: concept
name: Point process
msc: [60G55, 60G57, 60D05]
sources:
  - url: https://en.wikipedia.org/wiki/Point_process
same_as:
  wikidata: Q7208287
  wikipedia: Point process
---

## Summary

A point process is a random collection of points in a space, such as the line or the plane.
Each bounded region contains only finitely many of the points.
It is described as a random counting measure: for each region it gives the random number of points inside.
The [[Poisson point process|0MTNR28K60]] is the basic example.
Point processes model arrival times, positions of trees or stars, and eigenvalues of random matrices.

## Explanations

### L1 human

Throw a handful of sand on a floor and look at where the grains land.
The positions form a random pattern of points.
A point process is a model of such a pattern.
One describes it by counting: how many points fall in this square, how many in that disc.
The times at which customers enter a shop give a point process on the time line.